Question
$${\text{If }}\sqrt {1 + \frac{x}{{961}}} = \frac{{32}}{{31}}{\text{,}}$$ then the value of x is?
Answer: Option A
$$\eqalign{
& \sqrt {1 + \frac{x}{{961}}} = \frac{{32}}{{31}} \cr
& \left( {{\text{Squaring both sides}}} \right) \cr
& \Rightarrow 1 + \frac{x}{{961}} = \frac{{1024}}{{961}} \cr
& \Rightarrow \frac{{961 + x}}{{961}} = \frac{{1024}}{{961}} \cr
& \Rightarrow x = 1024 - 961 \cr
& \Rightarrow x = 63 \cr} $$
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$$\eqalign{
& \sqrt {1 + \frac{x}{{961}}} = \frac{{32}}{{31}} \cr
& \left( {{\text{Squaring both sides}}} \right) \cr
& \Rightarrow 1 + \frac{x}{{961}} = \frac{{1024}}{{961}} \cr
& \Rightarrow \frac{{961 + x}}{{961}} = \frac{{1024}}{{961}} \cr
& \Rightarrow x = 1024 - 961 \cr
& \Rightarrow x = 63 \cr} $$
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