Question
Download Solution PDFx2 - 7x + 1 = 0 এবং 0 < x < 1 হলে, x2 - \(\frac{1}{x^2}\) এর মান কত?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFঅনুসৃত সূত্র:
x + (1/x) = a
x - (1/x) = √(a2 - 4)
গণনা:
⇒ x2 - 7x + 1 = 0
x দ্বারা ভাগ করলে আমরা পাই:
⇒ x - 7 + (1/x) = 0
⇒ x + (1/x) = 7
এখন, (x - 1/x) = -√(49 - 4) = - √45 = - 3√5
[এখানে 0 < x < 1 অতএব x - (1/x) < 0]
⇒ x2 - (1/x2) = [x - (1/x)] [x + (1/x)]
⇒ 7 × (-3√5)
⇒ -21√5
∴ সঠিক উত্তর হল - 21√5
Mistake Points
এখানে 0 < x < 1
⇒ 1/x > 1
⇒ x - 1/x < 0
এইভাবে, x2 - (1/x2) = [x - (1/x)] [x + (1/x)] < 0
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