Answer:
x = 6
Step-by-step explanation:
Let's solve for x in the following equation:
√(2x - 3) + 3 = x
√(2x - 3) = x - 3 (Subtracting 3 at both sides)
(√(2x - 3))² = (x - 3)² (Raising at the second power at both sides)
2x - 3 = x² -6x + 9
0 = x² - 8x + 12 (Building quadratic equation)
0 = (x - 6) (x -2) (Factoring)
x₁ = 6
x₂ = 2
Proof of x = 6
√(2x - 3) + 3 = x
√(2 * 6 - 3) + 3 = 6
√(12 - 3) + 3 = 6
√9 + 3 = 6
3 + 3 = 6 ⇒ We proved that x = 6 is correct
Proof of x = 2
√(2x - 3) + 3 = x
√(2 * 2 - 3) + 3 = 2
√(4 - 3) + 3 = 2
√1 + 3 = 2
1 + 3 ≠ 6 ⇒ We proved that x = 2 is incorrect
