# Math Help - amazing problem

1. ## amazing problem

a,b,c are 3 real nos. Prove that the 3 numbers a^2+b+c, b^2+a+c, c^2+a+b cannot be perfect squares altogether.

2. ## Re: amazing problem

can you explain what you mean a little more? like, what do you mean by altogether?

3. ## Re: amazing problem

I believe he means "cannot all be perfect squares".

geniusgarvil seems to have a "genius" for posting problems that are "amazing" only because they are wrong. In this case, $a= b= c= -1+\sqrt{5}$
have $a^2+ b+ c= b^2+ a+ c= c^2+ a+ b= 4$.

4. ## Re: amazing problem

Originally Posted by geniusgarvil
a,b,c are 3 real nos. Prove that the 3 numbers a^2+b+c, b^2+a+c, c^2+a+b cannot be perfect squares altogether.
a = b = c = 0. 0 is a perfect square. Hmm.