SSC CGL Model Paper 14

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Question : 64 of 100

Marks: +1, -0

If

x={4√{ab}}/{√a+√b},

then what is the value of

{x+2√a}/{x-2√a} +{x+2√b}/{x-2√b}

(when a ≠ b)?

0
2
4
$(√a+√b)/(√a-√b)$

Solution:

x={4√{ab}}/{√a+√b}

⇒x/{2√a}={2√{ b}}/{√a+√b}

By componendo-dividendo rule,

⇒{x+2√a}/{x-2√a}

={2√b+√a+√b}/{2√b-√a-√b}

={3√b+√a}/{√b-√a}

Again,

x/{2√b}={2√a}/{√a+√b}

By componendo-dividendo rule,

⇒{x+2√b}/{x-2√b}

={2√a+√a+√b}/{2√a-√a-√b}

={3√a+√b}/{√a-√b}

∴{x+2√a}/{x-2√a} +{x+2√b}/{x-2√b}

={3√b+√a}/{√b-√a}+ {3√a+√b}/{√a-√b}

={3√b+√a-3√a-√b}/{√b-√a}

={2√b-2√a}/{√b-√a}=2

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