Question

qual o valor de x na equação (300/x-5)-(300/x)=2​

Answer 1

Resposta:

x = 80

Explicação passo-a-passo:

$\frac{300}{ \times - 5} - \frac{300}{ \times } = 2 \\ \frac{x - 5}{300} - \frac{ x}{300} = \frac{1}{2} \\ \frac{x - 5 + x}{300} = \frac{1}{2} \\ \frac{2x - 5}{300} = \frac{1}{2} \\ 2 \times (2x - 5) = 300 \times 1 \\ 4x - 20 = 300 \\ 4x = 300 + 20 \\ 4x = 320 \\ x = \frac{320}{4} = 80$

Answer 2

Resposta:

O valor de x na equação pode ser 30 ou -25.

Explicação passo-a-passo:

$\dfrac{300}{x-5}-\dfrac{300}{x}=2$

O m.m.c de $\mathbf{x-5}$ e $\mathbf{x}$ é igual a $\mathbf{x(x-5)}$. Logo,

$\dfrac{300x-300(x-5)}{x(x-5)}=2\\\\\\\dfrac{300x-300x+1500}{x(x-5)}=2\\\\\\\dfrac{1500}{x(x-5)}=2\\\\\\1500=2\;.\;x(x-5)\\\\\\1500=2\;.\;(x^2-5x)\\\\\\1500=2x^2-10x\\\\\\2x^2-10x-1500=0\\\\\\x^2-5x-750=0$

Usando Bhaskara,

$\text{Coeficientes: a = 1, b = -5 e c = -750}\\\\\Delta=b^2-4\;.\;a\;.\;c=(-5)^2-4\;.\;1\;.\;-750=25+3.000=3.025\\\\x=\frac{-b\pm\sqrt{\Delta}}{2\;.\;a}=\frac{-(-5)\pm\sqrt{3.025}}{2\;.\;1}=\frac{5\pm55}{2}\\\\x_1=\frac{5+55}{2}=\frac{60}{2}=30\\\\x_2=\frac{5-55}{2}=\frac{-50}{2}=-25$