Question

ORGANIZE E ENCONTRE AS RAÍZES DAS EQUAÇOES A) (2-X)(X+4)=8 B)(3X+4)(3X-4)=0 c468\c\bfdbxd

Answer 1

Explicação passo-a-passo:

a)

$\sf (2-x)\cdot(x+4)=8$

$2x+8-x^2-4x=8$

$\sf -x^2-2x+8-8=0$

$\sf -x^2-2x=0$

$\sf x\cdot(-x-2)=0$

• $\sf \red{x'=0}$

• $\sf -x-2=0~\rightarrow~\red{x"=-2}$

b)

$\sf (3x+4)\cdot(3x-4)=0$

$\sf (3x)^2-4^2=0$

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

$\sf 9x^2=16$

$\sf x^2=\dfrac{16}{9}$

$\sf x=\pm\sqrt{\dfrac{16}{9}}$

• $\sf \red{x'=\dfrac{4}{3}}$

• $\sf \red{x"=\dfrac{-4}{3}}$

Answer 2

Explicação passo-a-passo:

Equações do Segundo grau

$\mathtt{ A)~(2 - x)(x + 4)~=~8 }$

$\iff \mathtt{ 2x + \cancel{8}-x^2 - 4x~=~\cancel{8} }$

$\iff \mathtt{ -x^2 - 2x ~=~0 }$

$\iff \mathtt{ -x(x + 2)~=~0 }$

$\iff \mathtt{ \blue{ x~=~0~\vee~x~=~-2} }$

$\mathtt{ B) (3x+4)(3x - 4)~=~0 }$

$\iff \mathtt{ (3x)^2 - 4^2~=~0 }$

$\iff \mathtt{ 9x^2 - 16~=~0 }$

$\iff \mathtt{ x^2~=~\dfrac{16}{9} }$

$\iff \mathtt{ x~=~\pm \sqrt{ \dfrac{16}{9} }~=~\pink{\pm \dfrac{4}{3}} }$

Espero ter ajudado bastante!)