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Question 67
Given $$a+\frac{1}{a}$$=2 what is the value of $$a^{118}+\frac{1}{a^{117}}$$
Solution
If $$a+\frac{1}{a}$$=2
i.e; $$a^{2\ }+1=2a$$
i.e; $$a^{2\ }-2a+1=0$$
i.e; $$\left(a-1\right)^2=0$$
then, a = 1
$$a^{118}+\frac{1}{a^{117}} = 1^{118}+\frac{1}{1^{117}}=2$$
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