Question

Determine o valor de X na figura abaixo:​

Answer 1

Explicação passo-a-passo:

$\sf 8^2=x\cdot(x+6+6)$

$\sf 64=x\cdot(x+12)$

$\sf 64=x^2+12x$

$\sf x^2+12x-64=0$

$\sf \Delta=12^2-4\cdot1\cdot(-64)$

$\sf \Delta=144+256$

$\sf \Delta=400$

$\sf x=\dfrac{-12\pm\sqrt{400}}{2\cdot1}=\dfrac{-12\pm20}{2}$

$\sf x'=\dfrac{-12+20}{2}~\Rightarrow~x'=\dfrac{8}{2}~\Rightarrow~x'=4$

$\sf x"=\dfrac{-12-20}{2}~\Rightarrow~x"=\dfrac{-32}{2}~\Rightarrow~x"=-16$ (não serve)

Logo, x = 4