Question

If $\sqrt{(1+\frac{27}{169})}=(1+\frac{x}{13})$, then the value of $x$ is ____.

• A. $1$
• B. $3$
• C. $5$
• D. $7$

Answer 1

Answer: (A)

$1$

Given, $\sqrt{(1+\frac{27}{169})}=(1+\frac{x}{13})$

Squaring both sides, we get

$1+\frac{27}{169}=(1+\frac{x}{13}{)}^2$

$\Rightarrow 1+\frac{27}{169}=1+\frac{x^2}{169}+\frac{2x}{13}$

$\Rightarrow \frac{27}{169}=\frac{x^2}{169}+\frac{2x}{13}$

$\Rightarrow x^2+26x-27=0$

$\Rightarrow x^2+27x-x-27=0$

$\Rightarrow (x-1)(x+27)=0$

$\Rightarrow x=1,-27$ ....Only (A) option matches with one of our value