Question : If $x+ \frac{1}{9x}=4$, then the value of $9x^2+ \frac{1}{9x^2}$ is:
Option 1: 140
Option 2: 142
Option 3: 144
Option 4: 146
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Correct Answer: 142
Solution :
Given: $x+ \frac{1}{9x}=4$
Multiply by 3 on both sides of the above equation, we get,
⇒ $3x+ \frac{1}{3x}=12$
Squaring both sides of the above equation, we get,
⇒ $(3x+ \frac{1}{3x})^2=12^2$
⇒ $9x^2+ \frac{1}{9x^2}+2=144$
⇒ $9x^2+ \frac{1}{9x^2}=144–2$
⇒ $9x^2+ \frac{1}{9x^2}=142$
Hence, the correct answer is 142.
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