x2- 2√6- 5=0 হলে, x+ 1/x এর মান কত?

A 1√2

B 2/√3

C 2√3

D 1/√3

Solution

Correct Answer: Option C

দেওয়া আছে, x2- 2√6- 5=0
⇒ x2= 5 + 2√6
⇒ x2= 3 + 2√6 + 2
⇒ x2= (√3)^2 + 2. √3. √2 + (√2)^2
⇒ x2= (√3 + √2)^2
⇒ x= √(√3 + √2)^2
⇒ x= (√3 + √2)

 আবার,
1/x = 1/ (√3 + √2)
= (√3 - √2) /(√3 + √2)(√3 - √2)
= (√3 - √2) / 3-2
= (√3 - √2)

সুতরাং x + 1/x= (√3 + √2)+(√3 - √2)
                    = 2√3

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