Make b the subject of the formula:t=√a-b²/1+ab²
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))
To make b the subject of the formula t=√(a-b²)/(1+ab²), we need to isolate b on one side of the equation. Here are the steps to do that:
Step 1: Square both sides of the equation to remove the square root:
t² = (a - b²)/(1 + ab²)
Step 2: Multiply both sides of the equation by (1 + ab²) to remove the denominator:
t²(1 + ab²) = a - b²
Step 3: Distribute t² to both terms inside the parentheses:
t² + t²ab² = a - b²
Step 4: Move the b² term to the left-hand side of the equation by adding b² to both sides:
t² + t²ab² + b² = a
Step 5: Rearrange the terms to isolate b² on one side:
b² = a - (t² + t²ab²)
Finally,
b = √(a - (t² + t²ab²))