Question

se m e n são raizes de x²-6x+10=0,então ¹/m ¹/n vale:

Answer 1

$x^2-6x+10=0$

A = 1
B = -6
C = 10

lembrando que 
$\Bmatrix i^2= -1\\\\ i= \sqrt{-1} \end$


aplicando bhaskara
$x= \frac{-(-6)\pm \sqrt{(-6)^2-4*1*10} }{2*1} \\\\x= \frac{6\pm \sqrt{-4} }{2} \\\\x= \frac{6\pm \sqrt{4}* \sqrt{-1} }{2} \\\\\boxed{x= \frac{6\pm2i}{2} }\\\\\\ \bmatrix m = \frac{6-2i}{2}= 3-i\\\\n= \frac{6+2i}{2}= 3+i\end$

então
$\frac{1}{m} + \frac{1}{n} \\\\= \frac{1}{3-i} + \frac{1}{3+i} \\\\= \frac{1*(3+i) + 1*(3-i)}{(3-i)*(3+i)} \\\\= \frac{6}{3^2-i^2} = \frac{6}{9-(-1)} = \frac{6}{10}= \frac{3}{5}$