Question

What is the value of $x$ in the equation $\sqrt{1+\sqrt{1-\frac{2176}{2401}}}=1+\frac{x}{7}$?

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is B 1

$\sqrt{1+\sqrt{1-\frac{2176}{2401}}}=1+\frac{x}{7}$

$\Rightarrow \sqrt{1+\sqrt{\frac{2401-2176}{2401}}}=1+\frac{x}{7}$

$\Rightarrow \sqrt{1+\sqrt{\frac{225}{2401}}}=1+\frac{x}{7}$

$\Rightarrow \sqrt{1+\frac{\sqrt{225}}{\sqrt{2401}}}=1+\frac{x}{7}$

$\Rightarrow \sqrt{1+\frac{15}{49}}=1+\frac{x}{7}$

$\Rightarrow \sqrt{\frac{64}{49}}=1+\frac{x}{7}$

$\Rightarrow \frac{8}{7}=1+\frac{x}{7}$

$\Rightarrow \frac{x}{7}=\frac{8}{7}-1$

$\Rightarrow \frac{x}{7}=\frac{1}{7}$

$\Rightarrow x=\frac{1}{7}\times 7$

$\Rightarrow x=1$