To solve the equation \(\frac{x}{a} = \frac{y}{x}\) for \(x\), follow these steps:

1. **Cross multiply** to eliminate the fractions:
   \[
   x^2 = ay
   \]

2. **Take the square root** of both sides to solve for \(x\):
   \[
   x = \sqrt{ay}
   \]

   Note: The solution could be either positive or negative:
   \[
   x = \pm\sqrt{ay}
   \]

So, the solution is:
\[
x = \pm\sqrt{ay}
\]

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:
1. What if the equation was \(\frac{x}{a} = \frac{y}{b}\)? How would you solve for \(x\)?
2. How do you solve for \(x\) in the equation \(x^2 = y^2\)?
3. What happens if \(y\) is negative in the equation \(x/a = y/x\)?
4. Can you solve for \(y\) if the equation is \(\frac{x}{a} = \frac{y+b}{x}\)?
5. What if the equation was \(\frac{x}{a} = \frac{y + c}{x - d}\)? How would you solve for \(x\)?

**Tip:** When solving equations involving squares, remember to consider both the positive and negative roots unless otherwise specified.

Learn how to solve the equation x/a = y/x for x with a detailed step-by-step guide. This problem involves algebraic manipulation, including cross multiplication and solving equations with fractions. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation