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JAMB Mathematics 2020 Paper

Question : 29

Total: 40

\frac{\sqrt{2}}{x + \sqrt{2}}

\frac{1}{x - \sqrt{2}}

Solution:

Concept:

Cross-multiplication removes the fractions, leaving a simple equation to solve for

x

Explanation:

Start with

\frac{\sqrt{2}}{x + \sqrt{2}} = \frac{1}{x - \sqrt{2}}

Cross-multiply:

\sqrt{2}(x - \sqrt{2}) = x + \sqrt{2}

Expand:

x\sqrt{2} - 2 = x + \sqrt{2}

Rearrange terms with

x

on one side:

x\sqrt{2} - x = 2 + \sqrt{2}

Factor out

x

x(\sqrt{2} - 1) = 2 + \sqrt{2}

Divide by

\sqrt{2} - 1

x = \frac{2 + \sqrt{2}}{\sqrt{2} - 1}

Rationalise the denominator by multiplying top and bottom by

\sqrt{2} + 1

x = \frac{(2 + \sqrt{2})(\sqrt{2} + 1)}{(\sqrt{2} - 1)(\sqrt{2} + 1)}

Simplify the numerator and denominator:

x = \frac{2\sqrt{2} + 2 + 2 + \sqrt{2}}{2 - 1}

x = \frac{3\sqrt{2} + 4}{1}

x = 3\sqrt{2} + 4

Answer:

x = 3\sqrt{2} + 4

, which is option A.

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