a =√6 + √5 হলে, (a - 1)/a এর মান কত?

A 45√5

B 47√6

C 46√5

D 43√5

Solution

Correct Answer: Option C

a = √6 + √5 
=> 1/a = 1/(√6+√5)
=> 1/a = (√6 - √5)/{(√6+√5) (√6-√5)}
=> 1/a = (√6-√5)/{(√6) - (√5) }
=> 1/a = √6 - √5   

তাহলে,
a-(1/a) = √6+√5-√6+√5 = 2√5 
 এখন, a- 1/a
= a6/a - 1/a
= a - 1/a
= (a - 1/a) + 3.a.1/a (a - 1/a) 
 = (2√5) + 3.2√5
= 40√5 + 6√5
= 46√5

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