If $$\left( {x + \frac{1}{x}} \right) = 3,$$ then $$\left( {{x^2} + \frac{1}{{{x^2}}}} \right)$$ is = ?
A. $$\frac{{10}}{3}$$
B. $$\frac{{82}}{9}$$
C. 7
D. 11
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{Given,}} \cr & \left( {x + \frac{1}{x}} \right) = 3{\text{ }} \cr & {\text{On squaring both sides, we get}} \cr & {\left( {x + \frac{1}{x}} \right)^2} = {3^2} \cr & \Rightarrow {\left( {x + \frac{1}{x}} \right)^2} = 9 \cr & \Rightarrow {x^2} + \frac{1}{{{x^2}}} + 2 = 9 \cr & \Rightarrow {x^2} + \frac{1}{{{x^2}}} = 7 \cr} $$Related Questions on Simplification
A. 20
B. 80
C. 100
D. 200
E. None of these
A. Rs. 3500
B. Rs. 3750
C. Rs. 3840
D. Rs. 3900
E. None of these
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