What is the answer to solvefor x,sqrt(x/y)+sqrt(y/x)= 10/3 ?

The answer to solvefor x,sqrt(x/y)+sqrt(y/x)= 10/3 is x=9y,x= y/9

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solvefor x,sqrt(x/y)+sqrt(y/x)= 10/3

solve for

x, \frac{x}{y} + \frac{y}{x} = \frac{10}{3}

x = 9 y, x = \frac{y}{9}

Solution steps

\frac{x}{y} + \frac{y}{x} = \frac{10}{3}

Rewrite the equation with

\frac{x}{y} = u

and

x = u^{2} y

u + \frac{y}{u ^{2} y} = \frac{10}{3}

Solve

u + \frac{y}{u ^{2} y} = \frac{10}{3} : u = 3, u = \frac{1}{3} {y < 0 or y > 0}, u = \frac{5 - 34}{3} {y < 0 or y > 0}

u = 3, u = \frac{1}{3} {y < 0 or y > 0}, u = \frac{5 - 34}{3} {y < 0 or y > 0}

Substitute back

u = \frac{x}{y},

solve for

x

Solve

\frac{x}{y} = 3 : x = 9 y

Solve

\frac{x}{y} = \frac{1}{3} : x = \frac{y}{9}

Solve

\frac{x}{y} = \frac{5 - 34}{3} :

No Solution for

x \in R

x = 9 y, x = \frac{y}{9}

Verify Solutions:

x = 9 y

True

, x = \frac{y}{9}

True

The solutions are

x = 9 y, x = \frac{y}{9}

5 x + 1 - 25 = 0

5 x^{2} + 3 x - 33 = 3 x

x^{2} - 2 5 x + 4 = 0

x = - 1

2 p^{\frac{1}{3}} = 6

What is the answer to solvefor x,sqrt(x/y)+sqrt(y/x)= 10/3 ?
The answer to solvefor x,sqrt(x/y)+sqrt(y/x)= 10/3 is x=9y,x= y/9