x = √3 + √2 হলে x3+ 1/x3 এর মান কত?
Solution
Correct Answer: Option C
দেওয়া আছে, x = √3+√2
∴ 1/x = 1/(√3+√2)
= (√3-√2) / {(√3-√2) (√3+√2)}
= (√3-√2) / {(√3)2 - (√2)2}
= (√3-√2) / (3 - 2)
= (√3-√2) / 1
= (√3-√2)
∴ x+ 1/x = √3 + √2 + √3 - √2
= 2√3
প্রদত্ত রাশি = x3 + 1/x3
= (x + 1/x)3 - 3.x.1/x (x + 1/x)
= (2√3)3 - 3. 2√3
= 24√3 - 6√3
= 18√3
∴ 1/x = 1/(√3+√2)
= (√3-√2) / {(√3-√2) (√3+√2)}
= (√3-√2) / {(√3)2 - (√2)2}
= (√3-√2) / (3 - 2)
= (√3-√2) / 1
= (√3-√2)
∴ x+ 1/x = √3 + √2 + √3 - √2
= 2√3
প্রদত্ত রাশি = x3 + 1/x3
= (x + 1/x)3 - 3.x.1/x (x + 1/x)
= (2√3)3 - 3. 2√3
= 24√3 - 6√3
= 18√3
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