Question

Transpose the formula a² = (b² - c²) / (b²) to make b the subject

Answer 1

To transpose a² = (b² - c²) / (b²) for b, multiply through by b², add c² to both sides, factor b², divide by (a² + 1), and take the square root to get b = √(c² / (a² + 1)).

Step-by-step explanation:

To transpose the formula a² = (b² - c²) / (b²) to make b the subject, we can follow these steps:

1. Multiply both sides by b² to get rid of the denominator, which yields a² × b² = b² - c².
2. Add c² to both sides to isolate terms with b on one side: a² × b² + c² = b².
3. Factor out b² on the right-hand side: b²(a² + 1) = c².
4. Divide both sides by (a² + 1) to solve for b²: b² = c² / (a² + 1).
5. Finally, take the square root of both sides to solve for b: b = √(c² / (a² + 1)).

Therefore, the subject b has been isolated, and the transposed formula is b = √(c² / (a² + 1)).