CTET Paper II (Mathematics and Science) May 2016 Solved Paper

Concept:The given equation can be simplified by dividing and then squaring to obtain the required expression. Using the identity $(a+b)^2 = a^2 + b^2 + 2ab$ helps to isolate the desired term.Explanation:Start with $3x + \frac{1}{3x} = 6$. Divide the whole equation by 3: $x + \frac{1}{9x} = 2$. Square both sides: $(x + \frac{1}{9x})^2 = 4$. Expand the left side using the identity: $x^2 + \frac{1}{81x^2} + 2 \cdot x \cdot \frac{1}{9x} = x^2 + \frac{1}{81x^2} + \frac{2}{9}$. Set this equal to 4: $x^2 + \frac{1}{81x^2} + \frac{2}{9} = 4$. Subtract $\frac{2}{9}$ from both sides: $x^2 + \frac{1}{81x^2} = 4 - \frac{2}{9} = \frac{36}{9} - \frac{2}{9} = \frac{34}{9}$. Convert to mixed fraction: $\frac{34}{9} = 3\frac{7}{9}$.Answer:$3\frac{7}{9}$ (Option B)