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Algebra

Blazing goIITian

 Joined: 25 Jul 2011 Post: 322
27 Mar 2012 09:37:01 IST
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Solve it !!
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

Solve in integers: $x^3 + y^3 + z^3 = (x + y + z)^3$.

Hot goIITian

Joined: 10 Oct 2011
Posts: 120
27 Mar 2012 11:32:40 IST
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LOL LOL LOL fermats last theorem :)

Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
27 Mar 2012 14:25:36 IST
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x=0 y=0 z=0 ; x=0 y=-1 z=1 (you can permute this); General solution x=0 y=a z=-a where a is any integer

Scorching goIITian

Joined: 10 Feb 2012
Posts: 262
27 Mar 2012 14:40:33 IST
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there is infinite number of solution i.ex is any real or integer for all ...y+z=0 how i got this is on simplification of the above you can get an equation (x+y)(y+z)(x+z)=0 hence apply zero factor theorem here to get to the solution

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Joined: 1 Jun 2009
Posts: 1331
1 Apr 2012 00:56:49 IST
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(x + y + z)^3 = x^3  +  y^3  +  z ^3  +  3(x^2 y   + xy^2  +  x^2z   + xz^2   +  y^2z  +   yz^2)  + 6xyz

if (x + y + z)^3 = x^3  +  y^3  +  z ^3  then 3(x^2 y   + xy^2  +  x^2z   + xz^2   +  y^2z  +   yz^2)  + 6xyz =0

now just check this to be with hit and trial!!

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