Question

Tentukan himpunan penyelesaian dari pertidaksamaan berikut (x-2)² ‹ x-2

Answer 1

(x−2)2>x−2

x2−4x+4>x−2

Let's find the critical points of the inequality.

x2−4x+4=x−2

x2−4x+4−(x−2)=x−2−(x−2)(Subtract x-2 from both sides)

x2−5x+6=0

(x−2)(x−3)=0(Factor left side of equation)

x−2=0 or x−3=0(Set factors equal to 0)

x=2 or x=3

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x<2(Works in original inequality)

2<x<3(Doesn't work in original inequality)

x>3(Works in original inequality)

Answer:

x<2 or x>3

Answer 2

(x - 2)² < x - 2
x² - 4x + 4 < x - 2
x² - 4x - x + 4 + 2 < 0
x² - 5x + 6 < 0
(x - 2)(x - 3) < 0
x - 2 = 0
     x = 2
atau
x - 3 = 0
     x = 3

HP = {x | x < 2 atau x > 3, x ∈ R}