Question

Resolva a inequação: (x²-7x+2,5)/(x-2) > 3

Answer 1

Olá, boa madrugada!

Resposta:

$\boxed{\mathbf{\dfrac{10 - \sqrt{66}}{2} < x < 2 \ ou >\dfrac{10 + \sqrt{66}}{2}}}$

Resolução passo a passo:

$\math{\dfrac{(x^2 -7x +2,5)}{x - 2} > 3}$

$\math{\dfrac{x^2 -7x +2,5}{x - 2} + \dfrac{-3(x-2)}{x-2} > 0}$

$\math{\dfrac{x^2 -7x +2,5 -3(x-2)}{x-2}} > 0$

$\math{\dfrac{x^2 -10x +8,5}{x-2}} > 0$

_________

$\math{x^2-10x+8,5=0}$

Bhaskara...

a = 1

b = -10

c = 8,5

$\math{\dfrac{10+ - \sqrt{(-10)^2 -4 \times (1 \times 8,5)}}{2}}$

$\math{\dfrac{10 + - \sqrt{100-4 • 8,5} }{2}}$

$\math{\dfrac{10 + - \sqrt{100 - 34}}{2}}$

$\math{x=\dfrac{10 + - \sqrt{66}}{2}}$

_______________

$\math{x1=\dfrac{10 + \sqrt{66}}{2}}$

$\math{x2=\dfrac{10 - \sqrt{66}}{2}}$

$\math{x=\dfrac{10 - \sqrt{66} }{2}; \dfrac{10 + \sqrt{66}}{2}; 2}$

_______________

$\math{\dfrac{10 - \sqrt{66}}{2} < x < 2 \ ou >\dfrac{10 + \sqrt{66}}{2}}$

=================== Espero ter ajudado ===================

Abraços!