(x² + 1)² = 3x² হলে, (x³ + 1/x³) এর মান কত?
Solution
Correct Answer: Option C
(x2 + 1)2 = 3x2
⇒ x2 + 1 = √(3x2)
⇒ x2 + 1 = √3x
⇒ x2/x + 1/x = √3x/x
⇒ x + 1/x = √3
প্রদত্ত রাশি = x3 + 1/x3
= (x + 1/x)3 - 3.x.1/x(x + 1/x)
= (√3)3 - 3√3
= 3√3 - 3√3
= 0
⇒ x2 + 1 = √(3x2)
⇒ x2 + 1 = √3x
⇒ x2/x + 1/x = √3x/x
⇒ x + 1/x = √3
প্রদত্ত রাশি = x3 + 1/x3
= (x + 1/x)3 - 3.x.1/x(x + 1/x)
= (√3)3 - 3√3
= 3√3 - 3√3
= 0
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