Question

Resolva x/x-2 + 4/x-1=5
Em fórmula de baskara

Answer 1

$\frac{x}{x-2}+\frac{4}{x-1} = 5$

$\frac{x(x-1) +4 (x-2)}{(x-2)(x-1)} = 5$

$x(x-1) +4 (x-2) = 5 (x-2)(x-1)$

$x^2-x +4x-8 = (5x-10)(x-1)$

$x^2+3x-8 = 5x^2 -5x-10x+10$

$x^2+3x-8 = 5x^2 -15x+10$

$5x^2 -15x+10 = x^2+3x-8$

$5x^2-x^2 -15x-3x+10 +8= 0$

$4x^2 -18x+18= 0$ $\div (2)$

$2x^2 -9x+9= 0$

Temos,

$a = 2$, $b=-9$ e $c=9$

$\Delta = \sqrt{b^2-4 \cdot a \cdot c}$

$\Delta = \sqrt{(-9)^2-4 \cdot 2 \cdot 9}$

$\Delta = \sqrt{81-72}$

$\Delta = \sqrt{9}$

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

$x= \frac{-(-9) \pm \sqrt{9 }}{2 \cdot 2}$

$x= \frac{9 \pm 3}{4}$

$x' = \frac{9 + 3}{4} =\frac{12}{4} =3$

$x'' = \frac{9 - 3}{4} =\frac{6}{4} = \frac{3}{2}$

$S=\{ 3,\frac{3}{2}\}$