Question

Resolver
1- 3(x²-1)=2(x-1)²
2- 7+2x-4x(1-x)=x²-12
3- 6x²-20=x(5x+1)
4- (x-1)(x-5)-14+6x=2(3x-1)
5- 3x(3x+1)-4²x=-1
6- 2x-x²/2=4-x/3
7- x+4/5=10-x/5
8- 2x²/3-x/2=1-x/2+1

Answer 1

1) 3(x²-1)=2(x-1)²
3x²-3=2(x²-2x+1)
3x²-3=2x²-4x+2
3x²-2x²-3-2+4x=0
x²+4x-5=0
Δ=4²-4.1.-5
Δ=16+20=36
x'=-4+6/2=2/2=1
x''=-4-6/2=-10/2=-5
S={1;-5}
2) 7+2x-4x(1-x) = x²-12
7+2x-4x+4x²=x²-12
3x²-2x+19=0
Δ=-224
S= não existe
3) 6x²-20=x(5x+1)
6x²-5x²-x-20=0
x²-x-20=0
Δ=1-4.1.-20
Δ=1+80=81
x'=1+9/2=10/2=5
x''=1-9/2=-8/2=-4
S={5;-4}
4) (x-1)(x-5)-14+6x=2(3x-1)
x²-5x-x+5-14+6x=6x-2
x²-5x-x+5-14+2=0
x²-6x-7=0
Δ=(-6)²-4.1.(-7)
Δ=36+28=64
x'=6+8/2=14/2=7
x''=6-8/2=-2/2=-1
S={7;-1}
5) 3x(3x+1)-4²x=-1
9x²+3x-16x=-1
9x²+13x+1=0
Δ=13²-4.1.9
Δ=169-36=133
x'≈-13+11,5/18≈-2,5/18
x''≈-13-11,5/18≈-24,5/18
6) 2x-x²/2=4-x/3
6x-3x²=8-2x
-3x²+6x+2x-8=0
-3x²+8x-8=0
Δ=8²-4.-3.-8
Δ=64-96=-32
S=não existe
7) x+4/5=10-x/5
x+4=10-x
2x=6
x=6/2
x=3
8)4x²-3x=3-3x+6
4x²-3x+3x-3-6=0
4x²-9=0
x=√9/4
x=+-3/2