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Applications of quadratic equations - class-X
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What is the value of $x$ in the equation $\displaystyle \sqrt{1+\sqrt{1-\frac{2176}{2401}}}=1+\frac{x}{7}$?
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1
💡 Explanation:
$\displaystyle \sqrt{1+\sqrt{1-\cfrac{2176}{2401}}}=1+\cfrac{x}{7}$
$\Rightarrow \sqrt{1+\sqrt{\cfrac{2401-2176}{2401}}}=1+\cfrac{x}{7}$
$\Rightarrow \sqrt{1+\sqrt{\cfrac{225}{2401}}}=1+\cfrac{x}{7}$
$\displaystyle \Rightarrow \sqrt{1+\cfrac{\sqrt{225}}{\sqrt{2401}}}=1+\cfrac{x}{7}$
$\displaystyle \Rightarrow \sqrt{1+\cfrac{15}{49}}=1+\cfrac{x}{7}$
$\Rightarrow \sqrt{\cfrac{64}{49}}=1+\cfrac{x}{7}$
$\Rightarrow \cfrac{8}{7}=1+\cfrac{x}{7}$
$\Rightarrow \cfrac{x}{7}=\cfrac{8}{7}-1$
$\Rightarrow \cfrac{x}{7}=\cfrac{1}{7}$
$\Rightarrow x=\cfrac{1}{7}\times 7$
$\Rightarrow x=1$