x2 - 2x -1 = 0 হলে, x + 1/x = কত?
Solution
Correct Answer: Option C
x2 - 2x -1 = 0
⇒ x2 - 1 = 2x
⇒ (x2 - 1)/x = 2
⇒ x - 1/x = 2
আমরা জানি,
(x + 1/x)2 = (x - 1/x)2 + 4 x.1/x
⇒ (x + 1/x)2 = 22 + 4
⇒ (x + 1/x)2 = 4 + 4
⇒ (x + 1/x)2 = 8
⇒ (x + 1/x) = √8
⇒ (x + 1/x) = √(4 × 2)
∴ (x + 1/x) = 2√2
⇒ x2 - 1 = 2x
⇒ (x2 - 1)/x = 2
⇒ x - 1/x = 2
আমরা জানি,
(x + 1/x)2 = (x - 1/x)2 + 4 x.1/x
⇒ (x + 1/x)2 = 22 + 4
⇒ (x + 1/x)2 = 4 + 4
⇒ (x + 1/x)2 = 8
⇒ (x + 1/x) = √8
⇒ (x + 1/x) = √(4 × 2)
∴ (x + 1/x) = 2√2
Practice More Questions on Our App!
Download our app for free and access thousands of MCQ questions with detailed solutions