Solve for x in a radical equation.

The solution to the equation \sqrt{7 + \frac{3}{\sqrt{x}}} = 7 - \frac{9}{x} is x = \frac{9}{4}.

Answer

Here’s how to solve the equation:

Given the equation:

Let

. Then

, and the equation becomes:

Let

. Then

The equation can be rewritten as:

Also, we have

Let’s consider

. Then

and

. Since

is not a solution.

Let’s consider

. Then

and

. Since

is not a solution.

Let’s consider

. Then

and

. Since

is not a solution.

Let

and

.
Then

and

.
So

and

.
Thus,

.
If

and

.
If

and

.
So

.
Then

Final Answer: The final answer is

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Solve for x in a radical equation.

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Answer

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