Question

не решая уравнения x^2+4x-2=0, найдите значения выражения:   1/x1 + 1/x2

Answer 1

1/x1 + 1/x2 = (x1+ x2)/ (x1* x2) о теореме виета   x1+ x2= -4, x1* x2=-2,
-4/-2=2

Answer 2

$x^2+4x-2=0\D=16+8=8,sqrt{D}=2sqrt{2}\x_1=frac{-4-2sqrt{2}}{2}=-2-sqrt{2}, x_2=-2+sqrt{2}\frac{1}{x_1}+frac{1}{x_2}=frac{1}{-2-sqrt{2}}+frac{1}{-2+sqrt{2}}=frac{-2+sqrt{2}-2-sqrt{2}}{-(2+sqrt{2})(-2+sqrt{2})}=\=frac{-4}{-(2-4)}=frac{4}{-2}=-2$