Question 3

If $$x+\frac{1}{x}=-2$$, then find the value of $$x^{631}+\frac{1}{x^{632}}$$

Solution

Expression : $$x+\frac{1}{x}=-2$$

=> $$\frac{x^2+1}{x}=-2$$

=> $$x^2+2x+1=0$$

=> $$(x+1)^2=0$$

=> $$x+1=0$$

=> $$x=-1$$

$$\therefore$$ $$x^{631}+\frac{1}{x^{632}}$$

= $$(-1)^{631}+\frac{1}{(-1)^{632}}$$

= $$-1+1=0$$

=> Ans - (C)

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