109.
a) x²+22x-23=(x+23)(x-1)
x²+22x-23=0
D=484+92=576
x₁=-22-24=-23
2
x₂=-22+24=1
2
б) -3x²-8x+3=-3(x+3)(x- 1) =(x+3)(x-3x)
3
-3x²-8x+3=0
3x²+8x-3=0
D=64+4*3*3=100
x₁=-8-10=-3
6
x₂=-8+10= 1
6 3
в) -x²+18x-77=-(x-7)(x-11)=(7-x)(x-11)
-x²+18x-77=0
x²-18x+77=0
D=324-308=16
x₁=18-4=7
2
x₂=18+4=11
2
г) 7x²+9x+2=7(x+1)(x+2)=(x+1)(7x+2)
7
7x²+9x+2=0
D=81-56=25
x₁=-9-5=-1
14
x₂=-9+5=-2
14 7
110.
a) x²+2x-63 = -(x+9)(x-7) =-(x+9)(x-7)= - (x+9)
49-x² x²-49 (x-7)(x+7) x+7
x²+2x-63=0
D=4+4*63=4+252=256
x₁=-2-16=-9
2
x₂=-2+16=7
2
б) 6x²+x = x(6x+1) = x(6x+1) = x
6x²-17x-3 6(x+1)(x-3) (6x+1)(x-3) x-3
6
6x²-17x-3=0
D=289+4*6*3=289+72=361
x₁=17-19=-1
12 6
x₂=17+19=3
12
в) 8x-x² = x(8-x) = -x(x-8) = -x
x²-3x-40 (x+5)(x-8) (x+5)(x-8) x+5
x²-3x-40=0
D=9+160=169
x₁=3-13=-5
2
x₂=3+13=8
2
г) 5x²-12x+4 =5(x-0.4)(x-2)= (5x-2)(x-2) = x-2
25x²-4 (5x-2)(5x+2) (5x-2)(5x+2) 5x+2
5x²-12x+4=0
D=144-80=64
x₁=12-8=0.4
10
x₂=12+8=2
10