Question

A soma das raízes da equação

por favorrrrtt

Answer 1

$10^x=\frac{\sqrt[x]{1000^5} }{100}\\\\ 10^x.100=\sqrt[x]{1000^5}\\\\ 10^x.10^2=1000^{\frac{5}{x}}\\\\ 10^{x+2}=(10^3)^{\frac{5}{x}}\\\\ 10^{x+2}=10^{\frac{15}{x}}\\\\ x+2=\frac{15}{x}\\\\ x^2+2x=15\\ x^2+2x-15=0\\ \Delta=4+60=64\\\\ x=\frac{-2\pm \sqrt{64}}{2}\\\\ x_1=\frac{-2+8}{2}=3\\\\ x_2=\frac{-2-8}{2}=-5$

Soma das raízes: 3-5 = -2