What is the answer to sqrt((4x)/(1-\sqrt{x))}=3 ?

The answer to sqrt((4x)/(1-\sqrt{x))}=3 is x= 9/16

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sqrt((4x)/(1-\sqrt{x))}=3

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

x = \frac{9}{16}

Solution steps

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

\frac{256 x ^{4}}{x ^{2} - 4 x x + 6 x - 4 x + 1} = 6561

Use the following exponent property

x^{4} = (x)^{(4 \cdot 2)}, x^{2} = (x)^{(2 \cdot 2)}

\frac{256 ( x ) ^{8}}{( x ) ^{4} - 4 x ( x ) ^{2} + 6 ( x ) ^{2} - 4 x + 1} = 6561

Rewrite the equation with

x = u

\frac{256 u ^{8}}{u ^{4} - 4 u u ^{2} + 6 u ^{2} - 4 u + 1} = 6561

Solve

\frac{256 u ^{8}}{u ^{4} - 4 u u ^{2} + 6 u ^{2} - 4 u + 1} = 6561 : u = - 3, u = \frac{3}{4}

u = - 3, u = \frac{3}{4}

Substitute back

u = x,

solve for

x

Solve

x = - 3 :

No Solution for

x \in R

Solve

x = \frac{3}{4} : x = \frac{9}{16}

x = \frac{9}{16}

Verify Solutions:

x = \frac{9}{16}

True

The solution is

x = \frac{9}{16}

x + 3 - x - 2 = 5

x + 3 - x - 2 = 1

x^{2.5} = 20 x^{1.25}

(x - 4) - 5 (x - 4)^{\frac{1}{2}} = 6

5 x + 1 = x + 1

What is the answer to sqrt((4x)/(1-\sqrt{x))}=3 ?
The answer to sqrt((4x)/(1-\sqrt{x))}=3 is x= 9/16
Solve for x: sqrt((4x)/(1-\sqrt{x))}=3
The solution is x= 9/16