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Question 26

The value of $$x$$ which satisfies the equation $$\frac{\sqrt{x+5}+\sqrt{x-16}}{\sqrt{x+5}-\sqrt{x-16}} = \frac{7}{3}$$ is


Correct Answer: 20

Solution

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By componendo and dividendo, $$\frac{\sqrt{x+5}}{\sqrt{x-16}}=\frac{7+3}{7-3}=\frac{5}{2}$$, so $$\frac{x+5}{x-16}=\frac{25}{4}$$. Solving, $$4(x+5)=25(x-16)$$ gives $$420=21x$$, so $$x=20$$.

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