Question 14 Let \( x=\sqrt{10}+3 \). (a) Find the exact value of \( x+\frac{1}{x} \). (b) Hence, find the exact value of \( x^{2}+\frac{1}{x^{2}} \). (c) Hence, find the exact value of \( x^{4}+\frac{1}{x^{4}} \). (d) Hence, find the exact value of \( x^{8}+\frac{1}{x^{8}} \). (e) Explain the pattern you observe.
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Then, \( \frac{1}{x} = \frac{1}{\sqrt{10} + 3} \). Show more…
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