Question

Ecuatia:
3x^2+12x-21=0,x€R are solutiile x1,x2.Calculati x1^-2+x2^-2.

Answer 1

[tex] \frac{1}{x_1^2} + \frac{1}{x_2^2} = \frac{x_1^2+x_2^2}{x_1^2x_2^2}. relatia(1)\\ \\ x_1+x_2=- \frac{b}{a} =-4 \\ \\ P=x_1*x_2= \frac{c}{a} =-7 \\ \\ x1+x2=-4|^2, \\ \\ x_1^2+x_2^ 2+2x_1x_2=16 \\ \\ x_1^2+x_2^2=16-2P=16+14=30 \\ \\ In (1) \frac{30}{49} [/tex]
Mai verifica o data calculele.