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If $$x = 3 + \sqrt 8 {\text{,}}$$ then $${x^2} + \frac{1}{{{x^2}}}$$ is equal to?
Answer & Solution
Correct Answer:
Option
C
$$\eqalign{
& \Rightarrow x = 3 + \sqrt 8 \cr
& \Rightarrow {x^2} = 9 + 8 + 2 \times 3\sqrt 8 \cr
& \Rightarrow {x^2} = 17 + 6\sqrt 8 \cr
& \Rightarrow \frac{1}{{{x^2}}} = 17 - 6\sqrt 8 \cr
& \therefore {x^2} + \frac{1}{{{x^2}}} \cr
& = 17 + 6\sqrt 8 + 17 - 6\sqrt 8 \cr
& = 34 \cr} $$
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