Question

If $3x-\frac{1}{3x}=15$, find the value.

$9x^2+\frac{1}{9x^2}$

• A. $223$
• B. $227$
• C. $250$
• D. $235$

Answer 1

Answer: (B)

$227$

$9x^2+\frac{1}{9x^2}=?$

$3x-\frac{1}{3x}=15\left(Given\right)$

Squaring both sides, we have

${(3x-\frac{1}{3x})}^2={\left(15\right)}^2$

$\Rightarrow {\left(3x\right)}^2+{\left(\frac{1}{3x}\right)}^2-2\times 3x\times \frac{1}{3x}=225$

$\Rightarrow 9x^2+\frac{1}{9x^2}-2=225$

$\Rightarrow 9x^2+\frac{1}{9x^2}=225+2=227$

Hence, the correct answer is $227$.