Question 86

When [x + (1/x)] = 5, then what is the value of [x - (1/x)]?

Solution

Given : $$x+\frac{1}{x}=5$$

Squaring both sides, we get :

=> $$(x+\frac{1}{x})^2=(5)^2$$

=> $$x^2+\frac{1}{x^2}+2(x)(\frac{1}{x})=25$$

=> $$x^2+\frac{1}{x^2}=25-2=23$$ -----------------(i)

We know that, $$(x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-2(x)(\frac{1}{x})$$

Substituting value from equation (i),

=> $$(x-\frac{1}{x})^2=23-2=21$$

=> $$x-\frac{1}{x}=\pm \sqrt{21}$$

=> Ans - (D)

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