Question

$\frac{8-x}{2}-\frac{x+6}{2} =\frac{2x-11}{x-3}$ equação do 2 grau

Answer 1

Explicação passo-a-passo:

Equação do segundo grau:

$\frac{8-x}{2}-\frac{x+6}=\frac{2x-11}{x-3}$

$\frac{8-x-(x+6)}{2}=\frac{2x-11}{x-3}$

$\frac{8-x-x-6}{2}=\frac{2x-11}{x-3}$

$\frac{-2x+2}{2}=\frac{2x-11}{x-3}$

(-2x + 2) • ( x — 3 ) = (2x — 11) • 2

—2x² + 6x + 2x — 6 = 4x — 22

—2x² + 8x — 6 = 4x — 22

—2x² + 8x — 4x — 6 + 22 = 0

—2x² + 4x + 16 = 0

x² — 2x — 8 = 0

Coeficientes:

a = 1 , b = -2 , b = -8

Bhaskara:

$\large\boxed{\boxed{{x_{(1,2)}=\frac{-b\pm\sqrt{b^2-4.a.c}}{2.a}}}}}}$

Jogando os dados na formula teremos:

$x_{(1,2)}=\frac{-(-2)\pm\sqrt{(-2)^2-4.1.(-8)}}{2.1}$

$x_{(1,2)}=\frac{+2\pm\sqrt{4+32}}{2}$

$x_{(1,2)}=\frac{2\pm\sqrt{36}}{2}$

$x_{(1,2)}=\frac{2\pm\:6}{2}$

$x_{1}=\frac{2+6}{2}=\frac{8}{2}={\color{blue}{4}}$

$x_{2}=\frac{2-6}{2}=\frac{-4}{2}={\color{blue}{-2}}$

Sol: { -2 , 4 }

Espero ter ajudado bastante!)