solve for v^2

Question

LA=LB square root of 1-v^2/c^2

Answer 1

The equation LA = LB√[(1 - v²)/c²]

Cancel common terms.

A = B√[(1 - v²)/c²]

Squaring on each side.

A² = B²[(1 - v²)/c²]

A² = [B²(1 - v²)]/c²

Multiply each side by c².

A²c² = B²(1 - v²)

Divide each side by B².

(A²c²)/B² = 1 - v²

Subtract 1 from each side

(A²c²)/B² - 1 = - v²

Multiply each side by negative one.

v² = 1 - (A²c²)/B².