Question

Make x the subject
thank you​

Answer 1

`x =\sqrt{(a^6m)/(b^2)+n}`

General Formulas and Concepts:

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

Explanation:

Step 1: Define equation

`a\sqrt{(x^2-n)/(m) } =(a^2)/(b)`

Step 2: Solve for x

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