Question 35

If x = 1/(√2+1) then the value of $$x^{2}$$ + 2x - 1 is

Solution

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

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

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

=> $$x=\sqrt{2}-1$$

To find : $$x^2+2x-1$$

= $$(\sqrt{2}-1)^2+2(\sqrt{2}-1)-1$$

= $$(2+1-2\sqrt{2})+(2\sqrt{2}-2)-1$$

= $$3-3=0$$

=> Ans - (C)

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