\(x+\frac{1}{x}=2\) হলে \(x^4+\frac{1}{x^4}\)-এর মান কত?

Question

Question

This question was previously asked in

Bihar Prohibition Constable Memory Based Test (Held on: 14th May 2023)

Answer 1

প্রদত্ত:

x + 1/x = 2

অনুসৃত সূত্র:

a2 + b2 = (a + b)2 - 2ab

গণনা:

x2 + 1/x2 = (x + 1/x)2 - 2.x.1/x

⇒ x2 + 1/x2 = 22 - 2

⇒ x2 + 1/x2 = 2

এখন,

x4 + 1/x4 = (x2 + 1/x2)2 - 2

⇒ 22 - 2

⇒ 4 - 2

⇒ x4 + 1/x4 = 2

∴ x4 + 1/x4-এর মান 2