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.
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, $\displaystyle a= b= c= -1+\sqrt{5}$
have $\displaystyle a^2+ b+ c= b^2+ a+ c= c^2+ a+ b= 4$.