Question

Решите уравнение (4x-1)^2-(4x-1)-12=0

Answer 1

(4x-1)^2-(4x-1)-12=0

16x^2-8x+1-4x+1-12=0

16x^2-12x-10=0

2(8x^2-6x-5)=0

2(8x^2+4x-10x-5)=0

2(4x*(2x+1)-5(2x+1))=0

2(4x-5)*(2x+1)=0

(4x-5)*(2x+1)=0

4x-5=0            x1=5/4

2x+1=0           x2=-(1/2)

Answer 2

 (4x-1)^2-(4x-1)-12=0
4x-1=t
t²-t-12=0
D=1+48=49
t₁₂=(1+-7)/2= 4   -3
t₁=4    4x-1=4    4x=5   x=5/4
t₂=-3   4x-1=-3   4x=-2  x=-1/2