Question
Download Solution PDFযদি α এবং β , x2 – x – 1 = 0 এই সমীকরণের মূল হয় তবে α/β এবং β/α যে সমীকরণের মূল, সেই সমীকরণটি হবে :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত :
x2 – x – 1 = 0
অনুসৃত সূত্র :
যদি প্রদত্ত সমীকরণটি হয় ax2 + bx + c = 0
মূলগুলির যোগফল = -b/a
এবং মূলগুলির গুণফল = c/a
গণনা :
যদি α এবং β x2 – x – 1 = 0 এর মূল হয়, তবে
⇒ α + β = -(-1) = 1
⇒ αβ = -1
এখন, যদি (α/β) এবং (β/α) মূল হয়, তবে,
⇒ মূলগুলির যোগফল = (α/β) + (β/α)
⇒ মূলগুলির যোগফল = (α2 + β2)/αβ
⇒ মূলগুলির যোগফল= [(α + β)2 – 2αβ]/αβ
⇒ মূলগুলির যোগফল = (1)2 – 2(-1)]/(-1) = -3
⇒ মূলগুলির গুণফল = (α/β) × (β/α) = 1
এখন, সমীকরণটি হল-
⇒ x2 – (মূলগুলির যোগফল) x + মূলগুলির গুণফল= 0
⇒ x2 – (-3)x + (1) = 0
⇒ x2 + 3x + 1 = 0Last updated on Jun 2, 2025
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