x + (1/x) = 2 হলে x4 + 1/x4 এর মান -
Solution
Correct Answer: Option C
দেওয়া আছে,
x + (1/x) = 2
⇒ {x + (1/x)}² = 2² [বর্গ করে] [(a + b)² = a² + 2ab + b²]
⇒ x² + 2 × x × (1/x) + (1/x)² = 4
⇒ x² + (1/x)² = 4 - 2
⇒ {x² + (1/x)²}² = 2² [আবার বর্গ করে]
⇒ (x²)² + 2 × x² × (1/x²) + (1/x²)² = 4
⇒ x⁴ + 1/x⁴ = 4 - 2
∴ x⁴ + 1/x⁴ = 2
x + (1/x) = 2
⇒ {x + (1/x)}² = 2² [বর্গ করে] [(a + b)² = a² + 2ab + b²]
⇒ x² + 2 × x × (1/x) + (1/x)² = 4
⇒ x² + (1/x)² = 4 - 2
⇒ {x² + (1/x)²}² = 2² [আবার বর্গ করে]
⇒ (x²)² + 2 × x² × (1/x²) + (1/x²)² = 4
⇒ x⁴ + 1/x⁴ = 4 - 2
∴ x⁴ + 1/x⁴ = 2
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