Question

Make x the subjectthank you​

Answer 1

Answer:

$x =\sqrt{\frac{a^6m}{b^2}+n}$

General Formulas and Concepts:

• Order of Operations: BPEMDAS
• Equality Properties
• Exponent Power Rule: $(b^m)^n=b^{mn}$

Step-by-step explanation:

Step 1: Define equation

$a\sqrt{\frac{x^2-n}{m} } =\frac{a^2}{b}$

Step 2: Solve for x

1. Multiply a on both sides:                    $\sqrt{\frac{x^2-n}{m} } =\frac{a^3}{b}$
2. Square both sides:                              $\frac{x^2-n}{m} =(\frac{a^3}{b})^2$
3. Simplify:                                               $\frac{x^2-n}{m} =\frac{a^6}{b^2}$
4. Multiply m on both sides:                   $x^2-n =\frac{a^6}{b^2}m$
5. Add n to both sides:                           $x^2 =\frac{a^6}{b^2}m+n$
6. Simplify:                                               $x^2 =\frac{a^6m}{b^2}+n$
7. Square root both sides:                      $x =\sqrt{\frac{a^6m}{b^2}+n}$