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.

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- Sep 15th 2012, 09:14 AMgeniusgarvilamazing 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.

- Sep 15th 2012, 11:52 AMCoffeeBirdRe: amazing problem
can you explain what you mean a little more? like, what do you mean by altogether?

- Sep 15th 2012, 12:06 PMHallsofIvyRe: 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, $\displaystyle a= b= c= -1+\sqrt{5}$

have $\displaystyle a^2+ b+ c= b^2+ a+ c= c^2+ a+ b= 4$. - Sep 15th 2012, 02:59 PMrichard1234Re: amazing problem