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If a2 + b2 + c2 = 2(2a – 3b – 5c) – 38, find the value of (a – b – c).
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- 9
- 10
- 11
- 12
Correct Option: B
a2 + b2 + c2 = 4a – 6b – 10c – 38
⇒ a2 + b2 + c2 –4a + 6b + 10c + 38 = 0
⇒ a2 – 4a + 4 + b2 + 6b + 9 + c2 + 10c + 25 = 0
⇒ (a – 2)2 + (b + 3)2 + (c + 5)2 = 0
∴ a – 2 = 0 ⇒ a = 2
b + 3 = 0 ⇒ b = –3
c + 5 = 0 ⇒ c = –5
∴ a – b – c = 2 + 3 + 5 = 10