Đáp án:
`a, x=1,x=3,x=-1`
`b,x=-3,x=1,x=-7`
`c,x=5/2`
`d, x=4/3`
Giải thích các bước giải:
`a,`
`(x-1)^3 - 4 (x-1)=0`
`⇔ (x-1)^2 × (x-1)- 4 (x-1)=0`
`⇔ (x-1) [(x-1)^2-4]=0`
Trường hợp 1 :
`⇔x-1=0`
`⇔x=0+1`
`⇔x=1`
Trường hợp 2 :
`⇔(x-1)^2 -4=0`
`⇔ (x-1)^2=0+4`
`⇔(x-1)^2=4`
`⇔(x-1)^2=2^2` hoặc `(x-1)^2=(-2)^2`
`⇔x-1=2` hoặc `x-1=-2`
`⇔x=2+1` hoặc `x=-2+1`
`⇔x=3` hoặc `x=-1`
Vậy `x=1,x=3,x=-1`
`b,`
`(x+3)^3 - 16 (x+3)=0`
`⇔ (x+3) × (x+3)^2 - 16 (x+3)=0`
`⇔ (x+3) [(x+3)^2-16]=0`
Trường hợp 1 :
`⇔x+3=0`
`⇔x=0-3`
`⇔x=-3`
Trường hợp 2 :
`⇔ (x+3)^2-16=0`
`⇔ (x+3)^2=0+16`
`⇔ (x+3)^2=16`
`⇔(x+3)^2=4^2` hoặ c `(x+3)^2=(-4)^2`
`⇔x+3=4` hoặc `x+3=-4`
`⇔x=4-3` hoặc `x=-4-3`
`⇔x=1` hoặc `x=-7`
Vậy `x=-3,x=1,x=-7`
`c,`
`3 (x-2) + 1,25 = 2 (x-1)-1/4`
`⇔ 3x - 6 + 5/4 = 2x-2-1/4`
`⇔3x+(-6+5/4) = 2x + (-2-1/4)`
`⇔ 3x-19/4 = 2x -9/4`
`⇔ 3x-2x=19/4 - 9/4`
`⇔x=5/2`
Vậy `x=5/2`
`d,`
`2/3 - 1/2 (x+2)=1/3-x`
`⇔ 2/3 - 1/2x - 1 = -x+1/3`
`⇔ -1/2x + (2/3-1)=-x+1/3`
`⇔ -1/2x -1/3=-x+1/3`
`⇔ -1/2x+x=1/3+1/3`
`⇔ 1/2x=2/3`
`⇔x=2/3÷1/2`
`⇔x=4/3`
Vậy `x=4/3`
