Question

Solve for l:20%7D%20" id="TexFormula1" title="v = \frac{ \sqrt{l + t} }{2 \sqrt{l} } " alt="v = \frac{ \sqrt{l + t} }{2 \sqrt{l} } " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

l = t/4v² - 1

Step-by-step 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