Question
Download Solution PDFजर α आणि β ही (5 + √2) x2 - (4 + √5) x + (8 + 2√5) = 0 या द्विघाती समीकरणाची मुळे असतील , तर 2αβ/ (α + β) चे मूल्य आहे:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFवापरलेली संकल्पना:
द्विघात समीकरणासाठी, ax2 + bx + c = 0,
α + β = -b/a आणि αβ = c/a
गणना:
दिलेले समीकरण (5 + √2) x2 - (4 + √5) x + (8 + 2√5) = 0 आहे
या समीकरणाची ax2 + bx + c = 0 ने तुलना केल्यास आपल्याला मिळते
a = (5 + √2), b = - (4 + √5) आणि c = (8 + 2√5)
आता, αβ = (8 + 2√5)/(5 + √2) आणि α + β = (4 + √5)/(5 + √2)
आता, आपल्याला 2αβ/(α + β) चे मूल्य शोधावे लागेल
⇒ 2[(8 + 2√5)/(5 + √2)] / [(4 + √5)/(5 + √2)]
⇒ 2 [(8 + 2√5) (4 - √5)] / [(4 + √5)/(4 - √5)]
⇒ 2(32 + 8√5 - 8√5 - 10)/11
⇒ 44/11 = 4
∴ 2αβ/ (α + β) चे आवश्यक मूल्य 4 आहे.
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