Answer: x = { 2 ; 3 }
+) x² - 3 = x² - 1 - 2 = (x - 1)(x + 1) - 2
+) x² - 3 is divisible by x-1 but (x -1)(x + 1) is divisible by x-1
=> 2 must be divisible by x-1
=> x - 1 is divisor of 2
=> (x - 1) ∈ {-1; 1; 2; - 2;}
but x > 1 => x - 1 > 0
⇒ x - 1 = {1; 2; }
+) with x - 1 = 1 => x = 2
x - 1 = 2 => x = 3
Step-by-step explanation:
