Question 132

If $$x^{2}- 2\sqrt{10}x+ 1 = 0$$, then what is the value of $$x - \frac{1}{x}$$?

Solution

Given : $$x^2-2\sqrt{10}x+1=0$$

Dividing both sides by $$'x'$$

=> $$x+\frac{1}{x}=2\sqrt{10}$$

Squaring both sides, we get :

=> $$x^2+\frac{1}{x^2}+2(x)(\frac{1}{x})=40$$

=> $$x^2+\frac{1}{x^2}=40-2=38$$

=> $$(x-\frac{1}{x})^2+2(x)(\frac{1}{x})=38$$

=> $$(x-\frac{1}{x})^2=38-2=36$$

=> $$x-\frac{1}{x}=\sqrt{36}=6$$

=> Ans - (B)

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