Question

Rezolva in R ecuatiaa)7-6x-9x²=8
b)2(x-1)²=3x+2
c)(x-2)(x+3)=24
d)(x-3)(x+2)=14

Answer 1

a)7-6x-9x²=8-9x²-6x+7-8=0
-9x²-6x-1=0       ·(-1)
9x²+6x+1=0
Δ=36-36=0
x₁=x₂=-6/9=-2/3

b)2(x-1)²=3x+2
2(x²-2x+1)=3x+2
2x²-4x+2-3x-2=0
2x²-7x=0
x(2x-7)=0
x₁=0
2x-7=0
x₂=7/2

c)(x-2)(x+3)=24
x²+3x-2x-6=24
x²+x-6-24=0
x²+x-30=0
Δ=1+120=121
x₁=(-1+11)/2=5
x₁=5
x₂=(-1-11)/2=-6
x₂=-6

d)(x-3)(x+2)=14
x²+2x-3x-6=14
x²-x-6-14=0
x²-x-20=0
Δ=1+80=81
x₁=(1-9)/2=-4
x₁=-4
x₂=(1+9)/2=5
x₂=5