Question : If $\sqrt{1+\frac{x}{529}}=\frac{24}{23}$, then the value of $x$ is:
Option 1: 15
Option 2: 27
Option 3: 47
Option 4: 30
Correct Answer: 47
Solution :
$\sqrt{1+\frac{x}{529}}=\frac{24}{23}$
Squaring both sides,
$⇒1+\frac{x}{529}=\left(\frac{24}{23}\right)^2$
$⇒1+\frac{x}{529}=\frac{576}{529}$
$⇒\frac{x}{529}=\frac{576}{529}-1=\frac{47}{529}$
$\therefore x=47$
Hence, the correct answer is 47.
Related Questions
Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$; then what is the value of $x+\frac{1}{x}$?
Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$, what is the value of $(x^3+\frac{1}{x^3})$?
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