What is the answer to 1/(sqrt(x))+3sqrt(x)=8sqrt(x)-4 ?

The answer to 1/(sqrt(x))+3sqrt(x)=8sqrt(x)-4 is x=1

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1/(sqrt(x))+3sqrt(x)=8sqrt(x)-4

\frac{1}{x} + 3 x = 8 x - 4

x = 1

Solution steps

\frac{1}{x} + 3 x = 8 x - 4

Multiply both sides by

x

\frac{1}{x} x + 3 x x = 8 x x - 4 x

Simplify

1 + 3 (x)^{2} = 8 (x)^{2} - 4 x

Subtract

8 (x)^{2} - 4 x

from both sides

1 + 3 (x)^{2} - (8 (x)^{2} - 4 x) = 8 (x)^{2} - 4 x - (8 (x)^{2} - 4 x)

Simplify

1 - 5 (x)^{2} + 4 x = 0

Factor

1 - 5 (x)^{2} + 4 x : - (5 x + 1) (x - 1)

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

5 x + 1 = 0 or x - 1 = 0

Solve

5 x + 1 = 0 :

No Solution for

x \in R

Solve

x - 1 = 0 : x = 1

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

x + 3 - x - 2 = 6 x - 11

42 - 6 x = x - 7

9 x + 9 = x + 1

x + 7 - 3 x = 1

7 x + 18 = x + 4

What is the answer to 1/(sqrt(x))+3sqrt(x)=8sqrt(x)-4 ?
The answer to 1/(sqrt(x))+3sqrt(x)=8sqrt(x)-4 is x=1
Solve for x: 1/(sqrt(x))+3sqrt(x)=8sqrt(x)-4
The solution is x=1