If y = \;{2{x²+m}}{3N}, make x the subject of the formular

Correct Answer is : 9y2N2−4m2\;{{9y² N² - 4m}}{2}29y2N2−4m

Correct Answer is : 9y2N2−4m2\;{{9y² N² - 4m}}{2}29y2N2−4m

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WAEC Mathematics 2010 Paper

Question : 22

Total: 49

If y =

\;\frac{2\sqrt{x^{2}+m}}{3N}

, make x the subject of the formular

Solution:

Concept:

Isolate the square root, then square both sides to solve for

x

Explanation:

Start with the given equation:

y = \frac{2\sqrt{x^{2}+m}}{3N}

Multiply both sides by

3N

3Ny = 2\sqrt{x^{2}+m}

Divide both sides by

2

\frac{3Ny}{2} = \sqrt{x^{2}+m}

Square both sides to eliminate the square root:

\left(\frac{3Ny}{2}\right)^{2} = x^{2}+m

\frac{9N^{2}y^{2}}{4} = x^{2}+m

Subtract

m

from both sides:

x^{2} = \frac{9N^{2}y^{2}}{4} - m

x^{2} = \frac{9N^{2}y^{2} - 4m}{4}

Take the positive square root:

x = \frac{\sqrt{9N^{2}y^{2} - 4m}}{2}

Answer:

x = \frac{\sqrt{9y^{2}N^{2} - 4m}}{2}

, which is option B.

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