4
x1+x2=-p;x1*x2=-15
а)1/x1+1/x2=(x1+x2)/x1x2=p/15
б)x1²+x2²=(x1+x2)²-2x1x2=p²+30
в)x1/x2+x2/x1=(x1²+x2²)/x1x2=-(p²+30)/15
г)x1³+x2³=(x1+x2)(x1²+x2²-x1x2)=-p(p²+30+15)=-p(p²+45)
5
а)x²-6x+8=(x-4)(x+2)
x1+x2=6 U x1*x2=8
x1=4 U x2=2
б)8x²-6xy+y²=(9x²-6xy+y²)-x²=(3x-y)²-x²=(3x-y-x)(3x-y+x)=(2x-y)(4x-y)
в)x²-2x-1=(x²-2x+1)-2=(x-1)²-2=(x-1-√2)(x-1+√2)
6
10x²-13x-3=0
D=169+120=289
x1=(13-17)/20=-1/5 U x2=(13+17)/20=3/2
-2x²+x+3=0
D=1+24=25
x1=(-1-5)/(-4)=3/2 U x2=(-1+5)/(-4)=-1
(10x²-13x-3)/(-2x²+x+3)=10(x+1/5)(x-3/2)/-2(x-3/2)(x+1)=-5(x+1/5)/(x+1)=
=(-5x-1)/(x+1)=(5*6,2-1)/(-6,2+1)=30/(-5,2)=-300/52=-5 40/52=-5 10/13