very hard math riddles

[personia 4,036]

OK, if A*B = 2, then B= 2/A. If A-B = 3, then A - 2/A = 3, or in other words A^2-2 = 3A, or A^2-3A+2=0. The solutions are 2 and 1, using the quadratic formula.  If A = 2, then A^2 + B = A^2 + 2/A = 5. If A = 1, then it is 3. So the problem has two valid solutions.

Actually, the question has four valid solutions, because then you get a quadratic equation for the B as well. And then you have to square and add each A and B, meaning there are 4 solutions to the final question.

 

Also, you've done your working for that quadratic in the quote wrong. 

 

This is the correct working. It requires approximately 15 lines of working for the entire question if you're being thorough. 

 

AB=2

A-B=3

A=B+3

B(B+3)=2

B²+3B=2

B²+3B-2=0

Using the quadratic solving formula (see spoiler), solve the quadratic (or use a calc, if you're finding that tedious.)

https://en.wikipedia.org/wiki/Quadratic_formula

 

You should find that B=0.56, -3.56 (rounded to two dp).

 

Then, take this back into the original formula, A+B=3

 

Now, A+0.56=3

A=3-0.56

A=2.44

 

A-3.56=3

A=3+3.56

A=6.56

 

A=2.44, 6.56

 

Now substitute that into A²+B² to find X. 

 

X=6.2672, 18.6272, 43.3472, 55.7072.

 

If I have made a mistake in there, please tell me, and I'll be happy to go over what I've done and make it all right.

 

2,3 and 4 have already been answered correctly, so no need to figure them out.

Edited December 26, 2016 by personia

[delnina2 1,570]

1) 3B + B^2 = 2  --->  B = -2  or B = -1  

 

Therefore there is no answer for the first question due to the fact there is no such thing negative sqaure. 

 

The weird thing that everybody has a different answer ! 

Edited December 26, 2016 by delnina2

[personia 4,036]

lemme think a bit.

I actually got surprised by that one above, it looked easier than it was.

 

But please, give me some more. Or alternatively, I can give you some questions.

[personia 4,036]

red part does not look like the given question.

The question was "A - - B = 3"

Indeed, however I think he meant to write - and just got a typo and hit it twice. Given it is an exam question, it makes no sense for them to put - -B, instead of just putting + in (he said it was from papers that nobody got right.)

[BlueDragon_tamki 3,204]

1 and 2 is impossible

[personia 4,036]

1) 3B + B^2 = 2  --->  B = -2  or B = -1  

 

Therefore there is no answer for the first question due to the fact there is no such thing negative sqaure. 

 

The weird thing that everybody has a different answer ! 

That's not true. - numbers can be squared, they just can't be square rooted. -2²=4. -1²=1

 

Also, your answers are unfortunately wrong, as B²+3B=2 is not equal to -1 or -2.

 

B²+3B=2

 

B²+3B-2=0

 

-1²+3*-1-2=4

-2²+3*-2-2=4

 

This means that B cannot equal -1 or -2.

Edited December 26, 2016 by personia

[delnina2 1,570]

Furthermore, About question number four. You have a little problem there, due to the fact a book can not be a fraction. 

 

By the way here is a little question from me: 

 

I have five apples and three Oranges. 

 

I ate one of the furits.  Aferward I bought the same amount of these furits.

 

Later  I  gave Annie 3 of them. We ate togther 2 of them. What is the probablity that I have ate an Orange and Annie ate an Apple ? 

Edited December 26, 2016 by delnina2

[delnina2 1,570]

That's not true. - numbers can be squared, they just can't be square rooted. -2²=4. -1²=1

 

Also, your answers are unfortunately wrong, as B²+3B=2 is not equal to -1 or -2.

 

B²+3B=2

 

B²+3B-2=0

 

-1²+3*-1-2=4

-2²+3*-2-2=4

 

This means that B cannot equal -1 or -2.

You're right I have forgot to write rooted. 

 

What is the answer then ? I have an idea, maybe it's (sqaure rooted) 4 ? 

Edited December 26, 2016 by delnina2

[yonatanthesuper 314]

Actually, the question has four valid solutions, because then you get a quadratic equation for the B as well. And then you have to square and add each A and B, meaning there are 4 solutions to the final question.

 

Also, you've done your working for that quadratic in the quote wrong. 

 

This is the correct working. It requires approximately 15 lines of working for the entire question if you're being thorough. 

 

AB=2

A-B=3

A=B+3

B(B+3)=2

B²+3B=2

B²+3B-2=0

Using the quadratic solving formula (see spoiler), solve the quadratic (or use a calc, if you're finding that tedious.)

https://en.wikipedia.org/wiki/Quadratic_formula

 

You should find that B=0.56, -3.56 (rounded to two dp).

 

Then, take this back into the original formula, A+B=3

 

Now, A+0.56=3

A=3-0.56

A=2.44

 

A-3.56=3

A=3+3.56

A=6.56

 

A=2.44, 6.56

 

Now substitute that into A²+B² to find X. 

 

X=6.2672, 18.6272, 43.3472, 55.7072.

 

If I have made a mistake in there, please tell me, and I'll be happy to go over what I've done and make it all right.

 

2,3 and 4 have already been answered correctly, so no need to figure them out.

its a-b = 3 not a+b =3

Edited December 26, 2016 by yonatanthesuper

[personia 4,036]

its a-b = 3 not a+3

That's what I put...

[personia 4,036]

You're right I have forgot to write rooted. 

 

What is the answer then ? I have an idea, maybe it's (sqaure rooted) 4 ? 

 

 

Actually, the question has four valid solutions, because then you get a quadratic equation for the B as well. And then you have to square and add each A and B, meaning there are 4 solutions to the final question.

 

Also, you've done your working for that quadratic in the quote wrong. 

 

This is the correct working. It requires approximately 15 lines of working for the entire question if you're being thorough. 

 

AB=2

A-B=3

A=B+3

B(B+3)=2

B²+3B=2

B²+3B-2=0

Using the quadratic solving formula (see spoiler), solve the quadratic (or use a calc, if you're finding that tedious.)

https://en.wikipedia.org/wiki/Quadratic_formula

 

You should find that B=0.56, -3.56 (rounded to two dp).

 

Then, take this back into the original formula, A+B=3

 

Now, A+0.56=3

A=3-0.56

A=2.44

 

A-3.56=3

A=3+3.56

A=6.56

 

A=2.44, 6.56

 

Now substitute that into A²+B² to find X. 

 

X=6.2672, 18.6272, 43.3472, 55.7072.

 

If I have made a mistake in there, please tell me, and I'll be happy to go over what I've done and make it all right.

 

2,3 and 4 have already been answered correctly, so no need to figure them out.

[yonatanthesuper 314]

Furthermore, About question number four. You have a little problem there, due to the fact a book can not be a fraction. 

 

By the way here is a little question from me: 

 

I have five apples and three Oranges. 

 

I ate one of the furits.  Aferward I bought the same amount of these furits.

 

Later  I  gave Annie 3 of them. We ate togther 2 of them. What is the probablity that I have ate Orange and Annie ate an apple ? 

50% because if you both ate together 2 of the fruits then that means you ate an apple or an orange.

[personia 4,036]

I'll be back tomorrow for some more fun maths.

[gabriele02 3,813]

personia is pro

[delnina2 1,570]

50% because if you both ate together 2 of the fruits then that means you ate an apple or an orange.

Can you show me the way to the solution ? 

[delnina2 1,570]

Actually, the question has four valid solutions, because then you get a quadratic equation for the B as well. And then you have to square and add each A and B, meaning there are 4 solutions to the final question.

 

Also, you've done your working for that quadratic in the quote wrong. 

 

This is the correct working. It requires approximately 15 lines of working for the entire question if you're being thorough. 

 

AB=2

A-B=3

A=B+3

B(B+3)=2

B²+3B=2

B²+3B-2=0

Using the quadratic solving formula (see spoiler), solve the quadratic (or use a calc, if you're finding that tedious.)

https://en.wikipedia.org/wiki/Quadratic_formula

 

You should find that B=0.56, -3.56 (rounded to two dp).

 

Then, take this back into the original formula, A+B=3

 

Now, A+0.56=3

A=3-0.56

A=2.44

 

A-3.56=3

A=3+3.56

A=6.56

 

A=2.44, 6.56

 

Now substitute that into A²+B² to find X. 

 

X=6.2672, 18.6272, 43.3472, 55.7072.

 

If I have made a mistake in there, please tell me, and I'll be happy to go over what I've done and make it all right.

 

2,3 and 4 have already been answered correctly, so no need to figure them out.

Well, I have found that 

 

2.44/6.56 * 0.56 = Doesn't eqaul to 2. 

 

By the way I don't understand why did you do that "Now substitute that into A2+B2 to find X. "

 

More over B can't be negative (square rooted). I guess that this question has no solution since it's not the same A and B.

Edited December 26, 2016 by delnina2

[yonatanthesuper 314]

for annie its 66%

[delnina2 1,570]

for annie its 66%

Well Maybe, I didn't solve it myself... 

[yonatanthesuper 314]

actually its just 50% because there's just 2 different type of fruit and you can choose which one so annie an you ate 1 so there's 50% chance to be apple or orange.

[basenji7 1,199]

Furthermore, About question number four. You have a little problem there, due to the fact a book can not be a fraction. 

 

By the way here is a little question from me: 

 

I have five apples and three Oranges. 

 

I ate one of the furits.  Aferward I bought the same amount of these furits.

 

Later  I  gave Annie 3 of them. We ate togther 2 of them. What is the probablity that I have ate an Orange and Annie ate an Apple ? 

What does "afterward I bought the same amount of these fruits" mean? Also, did Annie eat fruits from what you gave her or from all the fruits in total? 

Edited December 26, 2016 by basenji7

[Tofu 6,773]

Furthermore, About question number four. You have a little problem there, due to the fact a book can not be a fraction. 

 

By the way here is a little question from me: 

 

I have five apples and three Oranges. 

 

I ate one of the furits.  Aferward I bought the same amount of these furits.

 

Later  I  gave Annie 3 of them. We ate togther 2 of them. What is the probablity that I have ate an Orange and Annie ate an Apple ? 

Actually the answer cannot be determined

You have not specified where you got the money from to buy the fruits. Also, no info is given on allergies/ preferences, so for all we know, Annie could be allergic to oranges or you may hate apples

[basenji7 1,199]

Actually, the question has four valid solutions, because then you get a quadratic equation for the B as well. And then you have to square and add each A and B, meaning there are 4 solutions to the final question.

 

Also, you've done your working for that quadratic in the quote wrong. 

 

This is the correct working. It requires approximately 15 lines of working for the entire question if you're being thorough. 

 

AB=2

A-B=3

A=B+3

B(B+3)=2

B²+3B=2

B²+3B-2=0

Using the quadratic solving formula (see spoiler), solve the quadratic (or use a calc, if you're finding that tedious.)

https://en.wikipedia.org/wiki/Quadratic_formula

 

You should find that B=0.56, -3.56 (rounded to two dp).

 

Then, take this back into the original formula, A+B=3

 

Now, A+0.56=3

A=3-0.56

A=2.44

 

A-3.56=3

A=3+3.56

A=6.56

 

A=2.44, 6.56

 

Now substitute that into A²+B² to find X. 

 

X=6.2672, 18.6272, 43.3472, 55.7072.

 

If I have made a mistake in there, please tell me, and I'll be happy to go over what I've done and make it all right.

 

2,3 and 4 have already been answered correctly, so no need to figure them out.

Idk if you did anything wrong in the middle, and I'm too lazy to check so I'll just tell you you're definitely wrong on your final answer - since there are two pairs of solutions, (a = (3+sqrt(17))/2, b = (-3+sqrt(17))/2) and (a = (3-sqrt(17))/2, b = (-3-sqrt(17))/2) (I used square roots for a more exact answer), you plug each PAIR into a^2 + b^2 to get TWO solutions. I think what you did was substitute each possibility of a and b, regardless of whether they fill the requirements together. If we square each number, however, we find that (3+sqrt(17))^2 = (-3-sqrt(17))^2 and (-3+sqrt(17))^2 = (3-sqrt(17))^2. So there's only one answer for x: 13. 

 

Edit: I found why. (a-b )^2 = a^2 + b^2 - 2ab, and since we know a-b and ab we get

3^2 = a^2 + b^2 - 4

9 + 4 = a^2 + b^2

a^2 + b^2 = 13. (God, I just did a whole bunch of work on the quadratics for nothing, didn't I?) 

Edited December 26, 2016 by basenji7

[delnina2 1,570]

What does "afterward I bought the same amount of these fruits" mean? Also, did Annie eat fruits from what you gave her or from all the fruits in total? 

For the first question - 5 apples and 3 oranges again. We both ate from the furits I gave her.

 

Actually the answer cannot be determined

You have not specified where you got the money from to buy the fruits. Also, no info is given on allergies/ preferences, so for all we know, Annie could be allergic to oranges or you may hate apples

:D That's right ! :3

Edited December 26, 2016 by delnina2

[Tofu 6,773]

For the first question - 5 apples and 3 oranges again. We both ate from the furits I gave her.

 

:D That's right ! :3

B)

[DonCarnage 1,270]

i am not sure what you said there,i didn't learned that stuff,the question i brought up is a random question i got on one of the papers that nobody was able to solve.

Well, I answered a random math question. Often, a polynomial has multiple roots.