Question

QUESTAO 6 QUESTÃO 06 Sabendo que (a + b)2 = 150 e que a? + b2 = 90, qual o valor de a.b? O a) 10 O b) 20 O c) 30 O d) 40 e) 50​

Answer 1

$\large\boxed{\begin{array}{l}\rm Sabendo~que~(a+b)^2=150~e~a^2+b^2=90,\\\rm qual~o~valor~de~a\cdot b?\\\rm a)10\\\rm b)20\\\rm c)30\\\rm d)40\\\rm e)50\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao:}\\\sf (a+b)^2=a^2+2ab+b^2\implies a\cdot b=\dfrac{(a+b)^2-(a^2+b^2)}{2}\\\\\sf a\cdot b=\dfrac{150-90}{2}\\\\\sf a\cdot b=\dfrac{60}{2}\\\\\sf a\cdot b=30\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~c}}}}\end{array}}$