Question
Download Solution PDFx2 - \(\frac{1}{x^2}\) = 4 \(\sqrt2\) எனில் x4 - \(\frac{1}{x^4}\) இன் மதிப்பு என்ன?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFx2 -1/x2 = 4√2
பயன்படுத்தப்படும் சூத்திரம்:-
(A + B)2 = A2 + B2 + 2AB
(A2 - B2) = (A+ B) (A - B)
கணக்கீடு:-
இருபக்கமும் வர்க்கப்படுத்தவும்
⇒ (x2 -1/x2)2 = (4√2 )2
⇒ x4 + 1/x4 - 2 = 32
⇒ x4 + 1/x4 = 34
இரு பக்கமும் 2 ஐ கூட்டவும்
⇒ x4 + 1/x4 + 2 = 34 +2
⇒ (x2 + 1/x2)2 = 62
⇒ (x2 + 1/x2) = 6 ....(1)
கேள்வியின்படி,
⇒ x4 - 1/x4 = (x2 + 1/x2) (x2 -1/x2)
⇒ (4√2) × 6 = 24√ 2
∴ எனவே தேவையான பதில் 24√ 2.
Last updated on Jun 11, 2025
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