x²-Sx+P=0
x²-7x+3=0
S=x1+x2= 7
P=x1•x2= 3
a) x1+x2=S=7
b) x1²•x2²= S²-2P = 7²-2•3=49-6=43
sau rezolvare in alt mod:
x1 soluție →x1²-7x1+3=0
x2 soluție→x2²-7x2+3=0
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"+"
x1²+x2²-7x1+(-7x²)+3+3=0
x1²+x2²-7(x1+x2)+6=0
x1²+x2²=7(x1+x2)-6
x1²+x2²=7•S-6
x1²+x2²=7•7-6
x1²+x2²=49-6
x1²+x2²=43
c)x1³+x2³=S³-3SP =7³-3•7•3=343-42=341
d) 1/x1 + 1/x2 = (x1+x2) / x1•x2 = S/P = - 7/3
