(x² + 1)² = 3x² হলে x³ + 1/x³ এর মান কত?
Solution
Correct Answer: Option C
(x² + 1)² = 3x²
⇒ x⁴ + 2x² + 1 = 3x²
⇒ x⁴ - x² + 1 = 0
ধরি, y = x² + 1/x²
তাহলে, x⁴ + 1 = y·x²
এখন, x⁴ - x² + 1 = 0 ⇒ (x⁴ + 1) - x² = 0
⇒ y·x² - x² = 0
⇒ (y - 1)x² = 0
⇒ y = 1
এখন, x³ + 1/x³ = (x + 1/x)(x² - 1 + 1/x²)
= (x + 1/x)(y - 1)
= (x + 1/x)(1 - 1)
= (x + 1/x) × 0
= 0
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