Answer:
Solution of the equation is
x = {1, (1 + √(-3))/2, (1 - √(-3))/2}
Step-by-step explanation:
Given equation:
3/(x-2) + 6 = √(x-2) + 8
Subtracting 8 from both sides:
3/(x-2) + 6 - 8 = √(x-2) + 8 - 8
3/(x-2) - 2 = √(x-2)
Taking square on both sides:
9/(x-2)² - 4 = x - 2
Adding 2 on both sides:
9/(x-2)² - 2 = x
Multiplying by (x-2)² on both sides:
9 - 2(x-2)² = x(x-2)²
9 - 2(x²- 2x + 4) = x(x²-2x+4)
9 - 2x² + 4x - 8 = x³ - 2x² + 4x
Adding 2x² - 4x on both sides:
9 - 8 = x³
x³ = 1
Taking cube root:
x = ∛1
The solution of the equation is thus the three cube roots of unity:
1, (1 + √(-3))/2 and (1 - √(-3))/2.
