Question

Sendo (a+b)^2=72 e ab=74, calcule o valor de a^2+b^2.

Answer 1

$(a+b)^{2}=a^{2}+2ab+b^{2}~~~~~~~(quadrado~da~soma)$

Como (a + b)² = 72 e ab = 74:

$72=a^{2}+2(74)+b^{2}\\\\72=a^{2}+148+b^{2}\\\\72-148=a^{2}+b^{2}\\\\\boxed{\boxed{a^{2}+b^{2}=-76}}$