Solve for l: v = ( √(l + t) )/(2 √(l) ) .....​

Question

Solve for l:

`v = ( √(l + t) )/(2 √(l) )`
.....​

Answer 1

l = t/4v² - 1

Explanation:

Given the expression

v = √l+t/2√l

We are to make l the subject of the formula as shown;

Cross multiply

2v√l = √l+t

Square both sides

(2v√l)² = (√l+t)²

4v²l = l+t

t = 4v²l - l

t = l(4v² - 1)

Divide both sides by 4v² - 1

t/4v² - 1 = l(4v² - 1)/4v² - 1

t/4v² - 1 = l

Swap

l = t/4v² - 1

Hence the required expression for l is t/4v² - 1