x2 - 3x + 1 = 0 হলে (x - 1/x)4 এর মান-
Solution
Correct Answer: Option C
দেওয়া আছে,
x2 - 3x + 1 = 0
⇒ x2 + 1 = 3x
⇒ x2/x + 1/x = 3x/x
∴ x + 1/x = 3
আমরা জানি,
(x - 1/x)2 = (x + 1/x)2 - 4.x.1/x
⇒ (x - 1/x)2 = 32 - 4
⇒ (x - 1/x)2 = 5
⇒ {(x - 1/x)2}2 = 52
∴ (x - 1/x)4 = 25
x2 - 3x + 1 = 0
⇒ x2 + 1 = 3x
⇒ x2/x + 1/x = 3x/x
∴ x + 1/x = 3
আমরা জানি,
(x - 1/x)2 = (x + 1/x)2 - 4.x.1/x
⇒ (x - 1/x)2 = 32 - 4
⇒ (x - 1/x)2 = 5
⇒ {(x - 1/x)2}2 = 52
∴ (x - 1/x)4 = 25
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