Question
Download Solution PDFवर्गमुळांना अनुसरून वर्ग समीकरणे \(2 + \sqrt 5 \) आणि \(2 - \sqrt 5\) ही आहेत
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेल्याप्रमाणेः,
दोन वर्गमूळ 2 + √5 आणि 2 - √5 आहेत.
वापरलेली संकल्पनाः
वर्ग समीकरणः
x2 - (वर्गमुळांची बेरीज)x + वर्गमुळांचा गुणाकार = 0
गणनाः
दोन वर्गमूळ A आणि B मानू.
⇒ A = 2 + √5 आणि B = 2 - √5
⇒ A + B = 2 + √5 + 2 - √5 = 4
⇒ A × B = (2 + √5)(2 - √5) = 4 - 5 = -1
तर समीकरण आहे
∴ x2 - 4x - 1 = 0
वर्ग समीकरणासाठी ax2 + bx + c = 0,
वर्गमुळांची बेरीज = (-ब / अ) = 4/1
वर्गमुळांचा गुणाकार = c / a = -1/1
नंतर, b = -4
तर, x च्या गुणकांचे चिन्ह ऋण आहे.
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