Question

Se considera ecuatia: x^2-4x+2=0
Sa se calculeze: a) x1^-1+x2^-1
b) 1 supra x1+1 +1 supra x2+1

Answer 1

Răspuns:

Explicație pas cu pas:

$x^{2}-4x+2=0,~~din~relatiile~Viete,~\left \{ {{x_{1}+x_{2}=4} \atop {x_{1}x_{2}=2}} \right. \\a)~{x_{1}^{-1}+x_{2}^{-1}=\frac{1}{x_{1}}+\frac{1}{x_{2}}=\frac{x_{1}+x_{2}}{x_{1}x_{2}} =\frac{4}{2} =2.~\\b)~\frac{1}{x_{1}+1}+\frac{1}{x_{2}+1}=\frac{x_{2}+1+x_{1}+1}{(x_{1}+1)(x_{2}+1)}=\frac{4+1+1}{x_{1}x_{2}+x_{1}+x_{2}+1} =$

$=\frac{6}{2+4+1} =\frac{6}{7}$