Question

stiind ca x1,x2 sunt solutiile ecuatiei x²+3x+1=0, calculati x1²+x2²

Answer 1

folosim relatiile lui Viete, x1+x2=-b/a si x1x2=c/a
$x_{1} ^{2}+ x_{2} ^{2} = ( x_{1}+ x_{2}) ^{2}-2 x_{1} x_{2}=9-2=7$

Answer 2

Solutiile ecuatiei sunt:
X1=(-3+√5)/2, x2=(-3-√5)/2
x1²+x2² = (-3+√5)²/4+(-3-√5)²/4
X1²+X2²=(7-3√5)/2+(7+3√5)/2=7
X1²+X2²=7