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Question 14
If $$x=\frac{\sqrt{5}+1}{\sqrt{5}-1}$$ and $$y=\frac{\sqrt{5}-1}{\sqrt{5}+1}$$, then what is the value of x-y ?
Solution
Given : $$x=\frac{\sqrt{5}+1}{\sqrt{5}-1}$$ and $$y=\frac{\sqrt{5}-1}{\sqrt{5}+1}$$
To find : $$x-y=?$$
Solution =Â $$(\frac{\sqrt{5}+1}{\sqrt{5}-1})-(\frac{\sqrt{5}-1}{\sqrt{5}+1})$$
= $$\frac{(\sqrt5+1)^2-(\sqrt5-1)^2}{(\sqrt5-1)(\sqrt5+1)}$$
= $$\frac{(6+2\sqrt5)-(6-2\sqrt5)}{(5-1)}$$
= $$\frac{4\sqrt5}{4}=\sqrt5$$
=> Ans - (B)
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