Question

Solve algebraically: x2 − x ≥ 6.

A. x ≥ 3 and x ≥ −2
B. x ≥ 3 or x ≤ −2
C. x ≤ 3 and x ≤ −2
D. x ≤ 3 or x ≥ −2

Answer 1

A) x ≥ 3 and x ≥ -2

The solution of the given equation

x ≥ 3 and x ≥ -2

Explanation:

Explanation:-

Given that x2 − x ≥ 6.

⇒ x² − x - 6.≥ 0

⇒ x² - 3 x + 2x -6 ≥ 0

⇒ x ( x-3) +2 ( x-3) ≥ 0

⇒ ( x -3) ( x+2) ≥ 0

x -3 ≥ 0 and (x +2) ≥0

x ≥ 3 and x ≥ -2

Final answer:-

The solution of the given equation

x ≥ 3 and x ≥ -2