What is the answer to 4/(sqrt(x))-6sqrt(x)=sqrt(x)-3 ?

The answer to 4/(sqrt(x))-6sqrt(x)=sqrt(x)-3 is x=1

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4/(sqrt(x))-6sqrt(x)=sqrt(x)-3

\frac{4}{x} - 6 x = x - 3

x = 1

Solution steps

\frac{4}{x} - 6 x = x - 3

Multiply both sides by

x

\frac{4}{x} x - 6 x x = x x - 3 x

Simplify

4 - 6 (x)^{2} = (x)^{2} - 3 x

Subtract

(x)^{2} - 3 x

from both sides

4 - 6 (x)^{2} - ((x)^{2} - 3 x) = (x)^{2} - 3 x - ((x)^{2} - 3 x)

Simplify

4 - 7 (x)^{2} + 3 x = 0

Factor

4 - 7 (x)^{2} + 3 x : - (7 x + 4) (x - 1)

- (7 x + 4) (x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

7 x + 4 = 0 or x - 1 = 0

Solve

7 x + 4 = 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

3 x + 3 - 1 = 8 - 2 x

y, x^{\frac{2}{3}} + y^{\frac{2}{3}} = 1

1 - \frac{1}{3 x ^{\frac{2}{3}}} = 0

y, x = 4 - y^{2}

2 x - 6 - x - 5 = x - 1

What is the answer to 4/(sqrt(x))-6sqrt(x)=sqrt(x)-3 ?
The answer to 4/(sqrt(x))-6sqrt(x)=sqrt(x)-3 is x=1
Solve for x: 4/(sqrt(x))-6sqrt(x)=sqrt(x)-3
The solution is x=1