Question

If $\sqrt{1+\frac{25}{144}}=1+\frac{x}{12}$, find the value of $x$.

• A. $5$
• B. $3$
• C. $2$
• D. $1$

Answer 1

Answer: (D)

$1$

Given: $\sqrt{1+\frac{25}{144}}=1+\frac{x}{12}$

Let us square both sides .

${\left(\sqrt{1+\frac{25}{144}}\right)}^2={(1+\frac{x}{12})}^2$

$\Rightarrow 1+\frac{25}{144}=1+\frac{x^2}{144}+\frac{2x}{12}$

$\Rightarrow \frac{144+25}{144}$= $\frac{x^2+24x+144}{144}$

$\Rightarrow x^2+24x-25=0$

$\Rightarrow x^2+25x-1x-25=0$

$\Rightarrow x(x+25)-1(x+25)$

$\Rightarrow (x+25)(x-1)$

$\Rightarrow x=-25$ and $x=1$

Since $x=-25$ is not possible so $x=1$

The value of x is $1$.