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Halp pls.

srsly

 

z8oza.jpg

 

USAMO ftw.

So far I managed to prove this part:

koFnPYB.png

 

 

ok den

 

a = √2, b=1&c=1

a2 + b2 + c2 = 4

ab+ bc + ac- abc = √2 + 1 > 2

 

the problem is false

sorry for choosing 1 as example up there tho lol

The yellow part is incorrect, because a²+b²+c²+abc has to be equal to 4.

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So far I managed to prove this part:

koFnPYB.png

From the given equation, we can then assume WLOG that b,c>1 or b,c<1...

so (b-1)(c-1)>0.

 

Now write a2+b2+c2+abc=4 as the quadratic equation a2+(bc)a+b2+c2-4=0. Solving gives

 

a=(-bc+sqrt(bc-4(b2+c2-4)))/2                       (we eliminate the negative solution)

=(-bc+sqrt((4-b2)(4-c2)))/2

 

halp pls now

I have a feeling C-S is going to come into play...

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Well.... i dont need any help as I am already a pro in what they are teaching at school :P

But the equation yall are asking is well, reeeaaalllly tough

Edited by tanker538N

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From the given equation, we can then assume WLOG that b,c>1 or b,c<1...

so (b-1)(c-1)>0.

 

Now write a2+b2+c2+abc=4 as the quadratic equation a2+(bc)a+b2+c2-4=0. Solving gives

 

a=(-bc+sqrt(bc-4(b2+c2-4)))/2                       (we eliminate the negative solution)

=(-bc+sqrt((4-b2)(4-c2)))/2

 

halp pls now

I have a feeling C-S is going to come into play...

I'll write down what I found so far later today. :)

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If somebody here is an Einstein please answer this question

(x + 2)2 + (y + 1)2 = 13

Find the equation of the tangent at ( 0 , 2) to the circle with equation 

( I don't know it  :P ) 

Edited by Darren4Turbo

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If somebody here is an Einstein please answer this question

(x + 2)2 + (y + 1)2 = 13

Find the equation of the tangent at ( 0 , 2) to the circle with equation

( I don't know it :P )

So easy. I could have solved it 3 years ago :)

Look Here

Edited by beaku

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If somebody here is an Einstein please answer this question

(x + 2)2 + (y + 1)2 = 13

Find the equation of the tangent at ( 0 , 2) to the circle with equation 

( I don't know it  :P ) 

jP5Sv6j.png

Hopefully I didn't make any miscalculations. :p

I'm sorry if I don't use the correct terminology. I get taught mathematics in Dutch. :p 

 

So easy. I could have solved it 3 years ago :)

http://imgur.com/r8bxvOV%22%5D

I think you've put the wrong link here as I can't see any image. 

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I think you've put the wrong link here as I can't see any image.

Yeah. Sorry. Thanks for pointing it out.

Fixed it.

BTW... When did you learn geometry?

Edited by beaku

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You can use binomial theorem to solve it.

Lol why does the Tanki forum love Binomial theorem so much? :D The question required the expression to be broken down to a x+(1/x) form. The answer is {x^2+(1/x^2)}+{x^3+(1/x^3)}. Atleast I hope so. 

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Yeah. Sorry. Thanks for pointing it out.

Fixed it.

BTW... When did you learn geometry?

I think I started having geometry in maths from the first year of secondary school. It's a subject that comes back every year on a higher level. :p

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I think I started having geometry in maths from the first year of secondary school. It's a subject that comes back every year on a higher level. :p

First year of secondary school?? You mean when you were 16?

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