Question
Download Solution PDFयदि x2 - 1/x2 = 4 \(\sqrt2\) , तो x4 - 1/x4 का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFx2 -1/x2 = 4√2
प्रयुक्त :-
(A + B)2 = A2 + B2 + 2AB
(A2 - B2) = (A+ B) (A - B)
गणना:-
दोनों पक्षों का वर्ग करने पर
⇒ (x2 -1/x2)2 = (4√2 )2
⇒ x4 + 1/x4 - 2 = 32
⇒ x4 + 1/x4 = 34
दोनों पक्षों में 2 जोड़ने पर
⇒ x4 + 1/x4 + 2 = 34 +2
⇒ (x2 + 1/x2)2 = 62
⇒ (x2 + 1/x2) = 6 ....(1)
प्रश्न के अनुसार,
⇒ x4 - 1/x4 = (x2 + 1/x2) (x2 -1/x2)
⇒ (4√2) × 6 = 24√ 2
∴ अभीष्ट उत्तर 24√ 2 है।
Last updated on Jun 11, 2025
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