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What is the solution to the equation below? 3/x-2+6=square root x-2 +8

User Quape
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2 Answers

1 vote

The solution to the equation is:

x = -0.84

How to solve the equation?

The equation is given as:


(3)/((x - 2)) + 6 = √(x - 2) + 8

Subtract 8 from both sides to get:


(3)/((x - 2)) - 2 = √(x - 2)

Square both sides to get:


(9)/((x - 2)^(2) ) -
(12)/((x - 2)) = (x - 2)


(9 - 12(x - 2))/((x - 2)^(2) ) = (x - 2)

Multiply both sides by (x - 2)² to get:

9 - 12x + 24 = (x - 2)³

33 - 12x = x³ - 6x² + 12x - 8

x³ - 6x² + 24x + 25 = 0

Using polynomial calculator, the value of x is: x = -0.84

User JasonMc
by
7.6k points
3 votes

Answer:

Solution of the equation is

x = {1, (1 + √(-3))/2, (1 - √(-3))/2}

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.

User DilbertDave
by
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