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Raushan Kumar

· started a discussion

· 1 Months ago

How to solve it traditionally (Question: 108038.0 )

How can we solve it without using option

Question:
If 2x = \(\sqrt[]{a}\ + \cfrac{1}{\sqrt[]{a}}\) , a > 0, then the value of \(\cfrac{\sqrt{x^2-1}}{x-\sqrt[]{x^2-1}}\)    is:  
Options:
A) (a – 1) 
B) a + 1
C) \(\cfrac{1}{2}(a + 1)\)
D) \(\cfrac{1}{2}(a - 1)\)
Solution:
Ans: (d)

Putting a = 4, we get : 

x= \(\cfrac{5}{4}\)

Now, 


Now, checking options, option (d) : 

\(\cfrac{1}{2}(a-1)=\cfrac{1}{2}(4-1)=\cfrac{3}{2}\)

Hence, option (d) is the right option.

Anuj Hatoneya

· commented

· 1 Months ago

by manual arithmetic. X=(a+1)/2roota ; X^2-1=(a-1)/2roota ; substitute and solve.
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