Question
Download Solution PDFx2 - \(\frac{1}{x^2}\) = 4 \(\sqrt2\) అయిన, x4 - \(\frac{1}{x^4}\) విలువ ఎంత?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFx2 -1/x2 = 4√2
ఉపయోగించిన సూత్రం:-
(A + B)2 = A2 + B2 + 2AB
(A2 - B2) = (A+ B) (A - B)
సాధన:-
ఇరువైపులా వర్గం చేయగా
⇒ (x2 -1/x2)2 = (4√2 )2
⇒ x4 + 1/x4 - 2 = 32
⇒ x4 + 1/x4 = 34
ఇరువైపులా 2 ను జోడించగా
⇒ x4 + 1/x4 + 2 = 34 +2
⇒ (x2 + 1/x2)2 = 62
⇒ (x2 + 1/x2) = 6 ....(1)
ప్రశ్న ప్రకారం,
⇒ x4 - 1/x4 = (x2 + 1/x2) (x2 -1/x2)
⇒ (4√2) × 6 = 24√ 2
∴ అవసరమైన సమాధానం 24√ 2.
Last updated on Jun 11, 2025
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