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Isolate the square root term by multiplying both sides by (n)/(2m).

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Answer

A=±L−3kT2n24m2A = \pm \sqrt{L - \frac{3kT^2 n^2}{4m^2}}

Step-by-step solution

5 steps

  1. Isolate the square root term by multiplying both sides by n2m\frac{n}{2m}.

    T=2mnL−A23kT = \frac{2m}{n} \sqrt{\frac{L - A^2}{3k}} Tn2m=L−A23k\frac{Tn}{2m} = \sqrt{\frac{L - A^2}{3k}}

  2. Eliminate the square root by squaring both sides of the equation.

    (Tn2m)2=(L−A23k)2\left(\frac{Tn}{2m}\right)^2 = \left(\sqrt{\frac{L - A^2}{3k}}\right)^2 T2n24m2=L−A23k\frac{T^2 n^2}{4m^2} = \frac{L - A^2}{3k}

  3. Multiply both sides by 3k3k to isolate the term (L−A2)(L - A^2).

    3k(T2n24m2)=L−A23k \left(\frac{T^2 n^2}{4m^2}\right) = L - A^2 3kT2n24m2=L−A2\frac{3kT^2 n^2}{4m^2} = L - A^2

  4. Rearrange the equation to make A2A^2 the subject.

    A2=L−3kT2n24m2A^2 = L - \frac{3kT^2 n^2}{4m^2}

  5. Take the square root of both sides to solve for AA.

    A=±L−3kT2n24m2A = \pm \sqrt{L - \frac{3kT^2 n^2}{4m^2}}
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