x=√3+√2 হলে , x2 +1/x2 এর মান কত?
Solution
Correct Answer: Option B
দেওয়া আছে,
x = √3 + √2
এখন, 1/x = 1/(√3 + √2)
= (√3 - √2)/(√3 + √2) (√3 - √2)
= (√3 - √2)/(3 - 2)
∴ 1/x = √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
= (4 × 3) - 2
= 12 - 2
= 10
x = √3 + √2
এখন, 1/x = 1/(√3 + √2)
= (√3 - √2)/(√3 + √2) (√3 - √2)
= (√3 - √2)/(3 - 2)
∴ 1/x = √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
= (4 × 3) - 2
= 12 - 2
= 10
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