Question
Download Solution PDFComprehension
निर्देश : निम्नलिखित प्रश्नों के लिए निम्नलिखित पर विचार करें :
द्विघात समीकरण
a2(b2 - c2)x2 + b2(c2 - a2)x + c2(a2 - b2) = 0 के मूल समान हैं (a2 ≠ b2 ≠ c2).
निम्नलिखित में से कौन सा कथन सही है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
दिया गया है:
⇒ a2 (b2 - c 2 ) x2 + b 2 (c 2 - a 2 ) x + c 2 (a 2 - b 2 ) = 0...(i)
अब समीकरण के मूल समान हैं:
तब D =0
⇒ [b2 (c 2 - a2 )]2 - 4a 2 c 2 (b 2 - c 2 ) (a 2 - b 2 ) = 0
⇒ b4 (c 2 - a 2 )2 - 4a 2 c 2 (b 2 - c 2 ) (a 2 - b 2 ) = 0
उपरोक्त समीकरण को हल करने पर, हमें प्राप्त होता है
⇒ b4 (c2 + a2 )2 = 4a 4 c 4
⇒ b 2 (a 2 + c 2 ) = 2a 2 c 2
⇒
⇒ a2 , b 2 और c 2 हरात्मक श्रेणी (HP) में हैं
∴ विकल्प (c) सही है।
Last updated on May 30, 2025
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