Question

Se x - y = 5 e xy = 14, então o valor da expressão x²+y² é; ​

Answer 1

$\displaystyle \sf \\\\ sabemos \ que : \\\\ \underbrace{\sf (x-y)^2}_{\displaystyle 5^2} = x^2+y^2-2\cdot \underbrace{\sf xy}_{\displaystyle 14} \\\\\\ 25 =x^2+y^2-28 \\\\ x^2+y^2=25+28 \\\\ \huge\boxed{\sf x^2+y^2 = 53 \ }\checkmark$