Question
Download Solution PDFयदि समीकरण x2 – x – 1 = 0 के मूल α और β हैं, तब α/β और β/α मूल वाला समीकरण क्या होगा?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया हुआ:
x2 - x - 1 = 0
उपयोग किया गया सूत्र:
यदि दिए गए समीकरण ax2 + bx + c = 0 है
फिर मूलों का योग = -b/a
मूलों का गुणनफल = c/a
गणना:
चूंकि समीकरण x2 – x – 1 = 0 के मूल α और β हैं, तब
⇒ α + β = -(-1) = 1
⇒ αβ = -1
अब, यदि (α/β) और (β/α) मूल हैं तब,
⇒ मूलों का योग = (α/β) + (β/α)
⇒ मूलों का योग = (α2 + β2)/αβ
⇒ मूलों का योग = {(α + β)2 – 2αβ}/αβ
⇒ मूलों का योग = {(1)2 – 2(-1)}/(-1) = -3
⇒ मूलों का गुणनफल = (α/β) × (β/α) = 1
अब, समीकरण है,
⇒ x2 – (मूलों का योग)x + मूलों का गुणनफल = 0
⇒ x2 – (-3)x + (1) = 0
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