Question

If (a+b)2 = 9 and (a−b)2 = 49, what is the value of a2+b2?

Answer 1

`(a+b)^2+(a-b)^2=a^2+2ab+b^2+a^2-2ab+b^2=2a^2+2b^2=\\ 2(a^2+b^2)\\\Downarrow\\ 2(a^2+b^2)=9+49\\ 2(a^2+b^2)=58\\ a^2+b^2=29`