Question
Download Solution PDFयदि a = 101, b = 102 और c = 103 है, तो a2 + b2 + c2 − ab − bc − ca = _______.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
a = 101, b = 102 और c = 103
प्रयुक्त सूत्र:
1/2[(a - b)2 + (b - c)2 + (c - a)2] = a2 + b2 + c2 − ab − bc − ca
गणना:
⇒ a2 + b2 + c2 − ab − bc − ca = 1/2[(a - b)2 + (b - c)2 + (c - a)2]
⇒ a2 + b2 + c2 − ab − bc − ca = 1/2[(101 - 102)2 + (102 - 103)2 + (103 - 101)2]
⇒ a2 + b2 + c2 − ab − bc − ca = 1/2[12 + 12 + 22]
⇒ a2 + b2 + c2 − ab − bc − ca = 1/2[6]
⇒ a2 + b2 + c2 − ab − bc − ca = 3
अभीष्ट मान 3 है।
Last updated on Jul 10, 2025
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