Question

Determine o valor de "m" na equação: 9x² + mx - 2 = 0. Sendo x, = -2/3

Answer 1

$\sf 9x^2+mx-2=0$

$\sf 9\cdot\left(-\dfrac{2}{3}\right)^2-\dfrac{2m}{3}-2=0$

$\sf 9\cdot\dfrac{4}{9}-\dfrac{2m}{3}-2=0$

$\sf 4-\dfrac{2m}{3}-2=0$

$\sf 12-2m-6=0$

$\sf 2m=6$

$\sf m=\dfrac{6}{2}$

$\sf m=3$

Answer 2

Oie, Td Bom?!

$9x {}^{2} + mx - 2 = 0$

• Substitua $x$ por $- \frac{2}{3}$ .

$9 \: . \: ( - \frac{2}{3} ) {}^{2} + m \: . \: ( - \frac{2}{3} ) - 2 = 0$

$9 \: . \: ( \frac{2}{3} ) {}^{2} + m \: . \: ( - \frac{2}{3} ) - 2 = 0$

$9 \: . \: ( \frac{2}{3} ) {}^{2} - m \: . \: \frac{2}{3} - 2 = 0$

$9 \: . \: ( \frac{2}{3} ) {}^{2} - \frac{2}{3} m - 2 = 0$

$9 \: . \: \frac{2 {}^{2} }{3 {}^{2} } - \frac{2}{3} m - 2 = 0$

$9 \: . \: \frac{4}{9} - \frac{2}{3} m - 2 = 0$

• Simplifica pelo MDC 9.

$4 - \frac{2}{3} m - 2 = 0$

$2 - \frac{2}{3} m = 0$

• Multiplicando tudo por 3.

$3(2 - \frac{2}{3} m) = 3 \: . \: 0$

$3 \: . \: 2 - 3 \: . \: \frac{2}{3} m = 0$

$6 - 3 \: . \: \frac{2}{3} m = 0$

• Simplifica pelo MDC 3.

$6 - 2m = 0$

$- 2m = - 6$

$m = - 6 \div ( - 2)$

$m = 3$

Att. Makaveli1996