Question 33

If $$3x - \frac{1}{3x} = 9$$, then what is the value of $$x^{2} + \frac{x^2}{81}$$?

Solution

Given : $$3x-\frac{1}{3x}=9$$

Dividing both sides by 3, => $$x-\frac{1}{9x}=3$$

Squaring both sides, we get :

=> $$(x-\frac{1}{9x})^2=(3)^2$$

=> $$x^2+\frac{1}{81x^2}-2(x)(\frac{1}{9x})=9$$

=> $$(x^2+\frac{1}{81x^2})-\frac{2}{9}=9$$

=> $$(x^2+\frac{1}{81x^2})=9+\frac{2}{9}$$

=> $$(x^2+\frac{1}{81x^2})=\frac{83}{9}$$

=> Ans - (B)

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