Question
Download Solution PDFदो संख्याओं का योग 9 है और उनके वर्गों का योग 41 है। संख्याएँ हैं:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया है:
दो संख्याओं का योग = 9
उन संख्याओं के वर्ग का योग = 41
गणना:
मान लीजिए दो संख्याएँ x और y हैं, इसलिए
\(x+y=9\) .... समीकरण 1
\(x^2+y^2=41\) .... समीकरण 2
समीकरण 1 से \(x = 9-y\), इस मान को समीकरण 2 में प्रतिस्थापित करने पर, हम प्राप्त करते हैं:
\({{(9-y)^2}+y^2=41}\\ 81+y^2-18y+y^2=41\\ 2y^2-18y+81-41=0\\2y^2-18y+40=0\\ y^2-9y+20=0\\ y^2-5y-4y+20=0\\y(y-5)-4(y-5)=0\\ (y-4)(y-5)=0\\ y-4=0\:or\:y-5=0\\y=4\:or\:y=5\)
इस प्रकार, y या तो 4 या 5 है।
समीकरण 1 में y का मान रखने पर,
1. \(x+4=9\\x=5\)
2. \(x+5=9\\x=4\)
इस प्रकार, x या तो 5 या 4 है।
अतः संख्याएँ 4 और 5 हैं।
Last updated on Jul 18, 2025
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