Solve the Reciprocal Equation: Finding X in 9/x = x

Question

$\frac{9}{x}=x$

00:00 Find X

00:03 Multiply by the denominator to eliminate the fraction

00:08 Any number multiplied by itself is actually squared

00:11 Extract the root

00:14 When extracting a root there are always 2 solutions (positive, negative)

00:17 And this is the solution to the question

To solve the equation $\frac{9}{x} = x$ , we will eliminate the fraction by multiplying both sides by $x$ , provided $x \neq 0$ .

Our steps are as follows:

Step 1: Multiply both sides by $x$ to obtain $9 = x^2$ .
Step 2: Rearrange the equation to standard quadratic form: $x^2 - 9 = 0$ .
Step 3: Recognize that this can be solved by factoring as a difference of squares: $(x - 3)(x + 3) = 0$ .
Step 4: Solve for $x$ by setting each factor to zero, giving $x - 3 = 0$ or $x + 3 = 0$ .
Step 5: Solve these equations to find $x = 3$ or $x = -3$ .

Thus, the solutions to the equation $\frac{9}{x} = x$ are $x = 3$ and $x = -3$ .

Therefore, the correct answer, which matches choice 3, is $x = \pm 3$ .

$x=\operatorname{\pm}3$