Question 64

If $$a+\frac{1}{a}+2$$ then the value of $$a^{37}-\frac{1}{a^{100}}$$

Solution

$$a+\ \frac{\ 1}{a}+2=0$$

$$a^2+1+2a=0$$

$$\left(a+1\right)^2=0$$

$$=$$> $$a=-1$$

Therefore, $$a^{37}-\ \frac{\ 1}{a^{100}}=\left(-1\right)^{37}-\ \frac{\ 1}{\left(-1\right)^{100}}$$

$$=-1-1$$

$$=-2$$

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