Question
Download Solution PDFयदि \({{a^2 + b^2 + c^2 - 1024} \over ab - bc - ca} = -2\) और a + b = 5c है, जहाँ c > 0, तो c का मान ________________है।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
\({{a^2 + b^2 + c^2 - 1024} \over ab - bc - ca} = -2\)
प्रयुक्त सूत्र:
(a + b - c)2 = a2 + b2 + c2 + 2ab - 2bc - 2ca
गणना:
प्रश्नानुसार
\({{a^2 + b^2 + c^2 - 1024} \over ab - bc - ca}\) = - 2
⇒ a2 + b2 + c2 - 1024 = -2ab + 2bc + 2ca
⇒ a2 + b2 + c2 + 2ab - 2bc - 2ca = 1024
⇒ (a + b - c)2 = 1024
⇒ a + b - c = 32
a + b = 5c रखने पर,
⇒ 5c - c = 32
⇒ 4c = 32
c = 8
∴ सही उत्तर विकल्प 1 है।
Last updated on Jul 10, 2025
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