x^3-x^2-4x+4

x^3-x^2-4x+4

x^3-x^2-4x+4
=x²(x-1)-4(x-1)
=(x-1)(x²-4)
=(x-1)(x+2)(x-2)

(√x-3)^2+√x^2-4x+4
Simplification

Greater than or equal to 0 under root sign
Then x-3 > = 0
x>=3
So x > 2
x-2>0
Then | X-2 | = X-2
Original formula = x-3 + √ (X-2) ^ 2
=x-3+|x-2|
=x-3+x-2
=2x-5

(x-2)(x-4)+4x(x-3)=0

Solution
(x-2)(x-4)+4x(x-3)=0
x²-6x+8+4x²-12x=0
That is, 5x & # 178; - 18x + 8 = 0
△=b²-4ac=164
∴x=(18+√164)/10=(9+√41)/5
x=(18-√164)/10=(9-√41)/5

How to solve | x Λ 2-4x + 3 | > x Λ 2-4 | + 3

|x^2-4x+3|＞x^2-4|x|+3
=>|(x-1)(x-3)| > x^2-4|x|+3
case1:for x < 0
(x-1)(x-3) > x^2+4x+3
8x < 0
x