What is the answer to 3sqrt(x)=8+3/(sqrt(x)) ?

The answer to 3sqrt(x)=8+3/(sqrt(x)) is x=9

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3sqrt(x)=8+3/(sqrt(x))

3 x = 8 + \frac{3}{x}

x = 9

Solution steps

3 x = 8 + \frac{3}{x}

Multiply both sides by

x

3 x x = 8 x + \frac{3}{x} x

Simplify

3 (x)^{2} = 8 x + 3

Subtract

8 x + 3

from both sides

3 (x)^{2} - (8 x + 3) = 8 x + 3 - (8 x + 3)

Simplify

3 (x)^{2} - 8 x - 3 = 0

Factor

3 (x)^{2} - 8 x - 3 : (3 x + 1) (x - 3)

(3 x + 1) (x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 x + 1 = 0 or x - 3 = 0

Solve

3 x + 1 = 0 :

No Solution for

x \in R

Solve

x - 3 = 0 : x = 9

x = 9

Verify Solutions:

x = 9

True

The solution is

x = 9

x = 500 - 245

4 x - 2 x + 1 = 1

x^{\frac{1}{2}} = 5^{2}

x^{2} = 1

- 2 x^{\frac{3}{4}} = - 16

What is the answer to 3sqrt(x)=8+3/(sqrt(x)) ?
The answer to 3sqrt(x)=8+3/(sqrt(x)) is x=9
Solve for x: 3sqrt(x)=8+3/(sqrt(x))
The solution is x=9