If $$x + \frac{1}{{9x}} = 4{\text{,}}$$   then $${\text{9}}{x^2} + \frac{1}{{9{x^2}}}$$   is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{ }}x + \frac{1}{{9x}} = 4 \cr & {\text{Multiply by 3 both side}} \cr & \Rightarrow {\text{3}}x + \frac{1}{{3x}} = 12 \cr & {\text{Squaring both sides}} \cr & \Rightarrow {\text{9}}{x^2} + \frac{1}{{9{x^2}}} + 2 \times 3x \times \frac{1}{{3x}} = 144 \cr & \Rightarrow {\text{9}}{x^2} + \frac{1}{{9{x^2}}} + 2 = 144 \cr & \Rightarrow {\text{9}}{x^2} + \frac{1}{{9{x^2}}} = 142 \cr} $$