What is the answer to sqrt(x/((1-x)))+sqrt(((1-x))/x)= 21/6 ?

The answer to sqrt(x/((1-x)))+sqrt(((1-x))/x)= 21/6 is x=0.08967…,x=0.91032…

Solve for x: sqrt(x/((1-x)))+sqrt(((1-x))/x)= 21/6

The solution is x=0.08967…,x=0.91032…

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\frac{x}{( 1 - x )} + \frac{( 1 - x )}{x} = \frac{21}{6}

x = 0.08967 \dots, x = 0.91032 \dots

Solution steps

\frac{x}{( 1 - x )} + \frac{( 1 - x )}{x} = \frac{21}{6}

Rewrite the equation with

\frac{x}{( 1 - x )} = u

and

x = \frac{u ^{2}}{1 + u ^{2}}

u + \frac{1 - ( \frac{u ^{2}}{1 + u ^{2}} )}{( \frac{u ^{2}}{1 + u ^{2}} )} = \frac{21}{6}

Solve

u + \frac{1 - ( \frac{u ^{2}}{1 + u ^{2}} )}{( \frac{u ^{2}}{1 + u ^{2}} )} = \frac{21}{6} : u \approx 0.31385 \dots, u \approx - 0.26556 \dots, u \approx 3.18614 \dots

u \approx 0.31385 \dots, u \approx - 0.26556 \dots, u \approx 3.18614 \dots

Substitute back

u = \frac{x}{( 1 - x )},

solve for

x

Solve

\frac{x}{( 1 - x )} = 0.31385 \dots : x = 0.08967 \dots

Solve

\frac{x}{( 1 - x )} = - 0.26556 \dots :

No Solution for

x \in R

Solve

\frac{x}{( 1 - x )} = 3.18614 \dots : x = 0.91032 \dots

x = 0.08967 \dots, x = 0.91032 \dots

Verify Solutions:

x = 0.08967 \dots

True

, x = 0.91032 \dots

True

The solutions are

x = 0.08967 \dots, x = 0.91032 \dots

6 x - 9 = x

k, q = (2 l + 2 k)^{\frac{1}{2}}

x = 5 - x \cdot 5

x^{\frac{2}{3}} = 2

x^{\frac{1}{2}} - 2 x + 4 = 0

What is the answer to sqrt(x/((1-x)))+sqrt(((1-x))/x)= 21/6 ?
The answer to sqrt(x/((1-x)))+sqrt(((1-x))/x)= 21/6 is x=0.08967…,x=0.91032…
Solve for x: sqrt(x/((1-x)))+sqrt(((1-x))/x)= 21/6
The solution is x=0.08967…,x=0.91032…