Question

Preciso de ajuda nessas duas contas:

A) x +$\frac{1}{x}$ = $\frac{5}{2}$


B) x +$\frac{1}{x-5}$ = 7

Answer 1

a)

$x+\frac{1}{x}=\frac{5}{2}\\ \\ 2x^2+2=5x\\ \\ 2x^2-5x+2=0\\ \\ \Delta=(-5)^2-4.2.2=25-16=9\\ \\ x=\frac{5\pm\sqrt9}{4}\\ \\ x=\frac{5\pm3}{4}\\ \\ x_1=\frac{1}{2}\\ \\ x_2=2$

b)

$x+\frac{1}{x-5}=7\\ \\ x(x-5)+1=7(x-5)\\ \\ x^2-5x=7x-35\\ \\ x^2-5x-7x+35=0\\ \\ x^2-12x+35=0\\ \\ \Delta=(-12)^2-4.1.35=144-140=4\\ \\ x=\frac{12\pm2}{2}\\ \\ x_1=5\\ \\ x_2=7$