Question

a)4x3-3x-1=0

b)(2x-1)(x2-1)=6(x+1)

Answer 1

a) 4x³-3x-1=0

x³+3x³-3x-1=0

x³-1+3x³-3x=0

(x³-1) +3x(x²-1)=0

(x-1)(x²+x+1) + 3x(x-1)(x+1)=0

(x-1)[(x²+x+1)+3x(x+1)]=0

(x-1)(x²+x+1+3x²+3x)=0

(x-1)(4x²+4x+1)=0

(x-1)(2x+1)²=0

x-1=0 ∨ (2x+1)²= 0

x=1         2x+1=0

2x=-1

x=-0,5

Z={-0,5 ; 1}

 

b)(2x-1)(x²-1)=6(x+1)

(2x-1)(x-1)(x+1)-6(x+1)=0

(x+1)[(2x-1)(x-1)-6]=0

(x+1)(2x²-2x-x+1-6)=0

(x+1)(2x²-3x-5)=0

x+1=0     ∨ 2x²-3x-5=0

x=-1       Δ=9-8*(-5) = 9+40=49

x=-1               x₁=(3+7)/4 = 2,5      x₂=(3-7)/4 = -4/4 = -1

Z={-1; 2,5}