Question

Fie ecuatia x²-3x+2=0. Calculati fara a rezolva ecuatia, folosind relatiile lui Viete urmatoarele sume : a) S1 = x1²+x2² b) S2= 1 supra x1+ 1 supra x2 c) S3= 1 supra x1²+ 1 supra x2²

Answer 1

Sper ca se intelege tot.

Answer 2

x1+x2=3 ; x1x2=2
a)S1=x1²+x2²=(x1+x2)²-2x1x2=3²-2*2=9-4=5
b)S2=1/x1+1/x2=(x1+x2)/x1x2=3/2
c)S3=1/x1²+1/x2²=(x1²+x2²)/x1²x2²=5/2²=5/4