Question
Download Solution PDFजर x 2 - 7x + 1 = 0, आणि 0 < x < 1 असेल, तर x 2 - \(\frac{1}{x^2}\) चे मूल्य किती आहे?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFवापरलेले सूत्र:
x + (1/x) = a
नंतर x - (1/x) = √(a 2 - 4)
गणना:
⇒ x 2 - 7x + 1 = 0
x ने भागल्यावर आपल्याला मिळते:
⇒ x - 7 + (1/x) = 0
⇒ x + (1/x) = 7
आता, (x - 1/x) = -√(49 - 4) = - √45 = - 3√5
[येथे 0 < x < 1 त्यामुळे x - (1/x) < 0]
⇒ x 2 - (1/x 2 ) = [x - (1/x)] [x + (1/x)]
⇒ 7 x (-3√5)
⇒ -21√5
∴ बरोबर उत्तर आहे - 21√5.
चूक गुण
येथे 0 < x < 1
⇒ 1/x > 1
⇒ x - 1/x < 0
अशा प्रकारे, x 2 - (1/x 2 ) = [x - (1/x)] [x + (1/x)] < 0
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