Question

calcule x e y na proporção x/2=y/3 sabendo que que xy=96​

Answer 1

Resposta:

$S = \{(8,12), (-8,-12)\}$

Explicação passo a passo:

$\frac{x}{2} = \frac{y}{3}\\3x = 2y~~^{(x)}\\3x^2 = 2xy\\3x^2 = 2(96)\\3x^2 = 192\\x^2 = \frac{192}{3}\\x^2 = 64\\\sqrt{x^2} = \sqrt{64}\\x = \pm 8\\\\x' = 8\\\frac{8}{2} = \frac{y'}{3}\\4 = \frac{y'}{3}\\y' = 4\times3\\y' = 12\\\\x'' = -8\\-\frac{8}{2} = \frac{y''}{3}\\-4 = \frac{y''}{3}\\y'' = 3(-4)\\y'' = -12\\\\S = \{(8,12), (-8,-12)\}$