Question

Os va os valores de g e h são raizes da equação x² - 6x + 10 = 0 então( 1 sobre G +1 sobre H) vale quanto?

Answer 1

$x^2-6x+10=0\\ \delta=-6^2-4*1*10=-4\\\\ x=\frac{6\frac{+}{-}\sqrt{-4}}{2}\\\\ \sqrt{4}=\sqrt{4i^2}\\\\ x=\frac{6\frac{+}{-}\sqrt{4i^2}}{2}\\\\ x=\frac{6\frac{+}{-}2i}{2} \\\\ x=3\frac{+}{-}i\\ x_1=3+i=g \ \ \ \ \ x_2=3-i=h\\\\\\ \frac{1}{g}+\frac{1}{h}\\\\ \frac{1}{3+i}+\frac{1}{3-i}\\\\ \frac{(3-i)+(3-i)}{3^2-i^2}\\\\ \frac{6}{10} = \frac{3}{5}$

Resposta $\frac{3}{5}$