Make b the subject of the formula:t=√a-b²/1+ab²

Answer 1

To make b the subject of the formula, we need to rearrange the formula to isolate b on one side.

Given formula: t = √(a - b²) / (1 + ab²)

Step 1: Square both sides of the equation in order to eliminate the square root:
t² = (a - b²) / (1 + ab²)

Step 2: Multiply both sides of the equation by (1 + ab²) to eliminate the denominator:
t²(1 + ab²) = a - b²

Step 3: Expand the equation:
t² + t²ab² = a - b²

Step 4: Move the b² terms to one side of the equation:
t² + t²ab² + b² = a

Step 5: Rearrange the equation to isolate b²:
b² = a - t² - t²ab²

Step 6: Divide both sides of the equation by (1 + ab²):
b² / (1 + ab²) = (a - t² - t²ab²) / (1 + ab²)

Step 7: Simplify the right side of the equation:
b² / (1 + ab²) = a / (1 + ab²) - t² / (1 + ab²) - t²ab² / (1 + ab²)

Step 8: Take the square root of both sides of the equation:
b = √(a / (1 + ab²) - t² / (1 + ab²) - t²ab² / (1 + ab²))

Therefore, b is the subject of the formula: b = √(a / (1 + ab²) - t² / (1 + ab²) - t²ab² / (1 + ab²))