Answer:
[tex]x =\sqrt{\frac{a^6m}{b^2}+n}[/tex]
General Formulas and Concepts:
- Order of Operations: BPEMDAS
- Equality Properties
- Exponent Power Rule: [tex](b^m)^n=b^{mn}[/tex]
Step-by-step explanation:
Step 1: Define equation
[tex]a\sqrt{\frac{x^2-n}{m} } =\frac{a^2}{b}[/tex]
Step 2: Solve for x
- Multiply a on both sides: [tex]\sqrt{\frac{x^2-n}{m} } =\frac{a^3}{b}[/tex]
- Square both sides: [tex]\frac{x^2-n}{m} =(\frac{a^3}{b})^2[/tex]
- Simplify: [tex]\frac{x^2-n}{m} =\frac{a^6}{b^2}[/tex]
- Multiply m on both sides: [tex]x^2-n =\frac{a^6}{b^2}m[/tex]
- Add n to both sides: [tex]x^2 =\frac{a^6}{b^2}m+n[/tex]
- Simplify: [tex]x^2 =\frac{a^6m}{b^2}+n[/tex]
- Square root both sides: [tex]x =\sqrt{\frac{a^6m}{b^2}+n}[/tex]
