Question

ASSINALE A ALTERNATIVA QUE APRESENTA AS RAIZES DA EQUAÇÃO 9 x²- 24 x + 16 = 0 *

1-) X’= 4/3 E X” =3/4
2-) X’=X” = 4/3
3-) X’= X” = 3/4
4-) X’= 4/3 E X” = 4
5-) X’= 4 E X” =3

Answer 1

Explicação passo a passo:

$\sf 9x^2 - 24x + 16 = 0$

coeficientes: a = 9, b = - 24, c = 16

$\sf \Delta = b^2 - 4ac$

$\sf \Delta = (-24)^2 - 4*(9)*(16)$

$\sf \Delta = 576 - 576$

$\sf \Delta = 0$

$\sf x = \dfrac{- b \pm \sqrt{\Delta}}{2a}$

$\sf x = \dfrac{- (-24) \pm \sqrt{0}}{2*(9)} \Rightarrow x = \dfrac{24 \pm 0}{18}$

$\sf x' = \dfrac{24+0}{18} \Rightarrow x' = \dfrac{24\div6}{18\div6} \Rightarrow x' = \red{\dfrac{4}{3}}$

$\sf x'' = \dfrac{24-0}{18} \Rightarrow x'' = \dfrac{24\div6}{18\div6} \Rightarrow x'' = \red{\dfrac{4}{3}}$

raizes: 4/3

o conjunto solução é: $\mathbf{ S = \bigg\{\dfrac{4}{3}\bigg\}}$

>>> Alternativa 2)