Question

Daca x1, x2 sunt radacinile ecuatiei: x²+3x-10=0, fara a rezolva ecuatia, sa se calculeze:
a) 1supra x1+1+1 supra x2+1
b) 1 supra x1²+3x1+2+1 supra x2²+3x2+2

Answer 1

Iti pot raspunde doar la punctul a)$\frac{1}{ x_{1} +1 } +\frac{1}{ x_{2}+1 }= \frac{x_{1}+1+ x_{2}+1 }{( x_{1} +1)(x_{2}+1)} = \frac{ x_{1}+ x_{2}+2 }{(x_{1}* x_{2})+ (x_{1}+ x_{2}) +1 } \\ x_{1} + x_{2} =- \frac{b}{a} =- \frac{3}{1} =-3 \\ x_{1} * x_{2} = \frac{c}{a}= \frac{-10}{1} =-10 \\ \frac{ x_{1}+ x_{2}+2 }{(x_{1}* x_{2})+ (x_{1}+ x_{2}) +1 }=...=- \frac{1}{12}$