x = √3 + √2 হলে x² + 1/x² এর মান কত?
Solution
Correct Answer: Option A
x =√3 + √2
=> 1/x = 1/√3+√2
= (√3+√2)/(√3+√2)(√3-√2)
= √3 - √2/ (√3)2 - (√2)2
= √3 - √2
∴ x + 1/x = √3 + √2 + √3 -√2
= 2√3
∴ x2 + 1/x2 = (x+1/x )2 - 2.x.1/x
= (2√3)2 - 2
= 12 - 2
= 10
=> 1/x = 1/√3+√2
= (√3+√2)/(√3+√2)(√3-√2)
= √3 - √2/ (√3)2 - (√2)2
= √3 - √2
∴ x + 1/x = √3 + √2 + √3 -√2
= 2√3
∴ x2 + 1/x2 = (x+1/x )2 - 2.x.1/x
= (2√3)2 - 2
= 12 - 2
= 10
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