Question
Download Solution PDFIf a2 + 4b2 + 49c2 + 18 = 2 (2b + 28c – a), then the value of (3a + 2b + 7c) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFa2 + 4b2 + 49c2 + 18 = 2 (2b + 28c – a)
⇒ a2 + 4b2 + 49c2 + 18 = 4b + 56c – 2a
⇒ (a2 + 2a + 1) + (4b2 – 4b + 1) + (49c2 – 56c + 16) = 1 + 1 + 16 – 18
⇒ (a + 1)2 + (2b – 1)2 + (7c – 4)2 = 0
⇒ a + 1 = 0, 2b – 1 = 0, 7c – 4 = 0
⇒ a = -1, b = ½, c = 4/7
(3a + 2b + 7c) = (3 × (-1) + 2 × (1/2) + 7 × (4/7)) = -3 + 1 + 4 = 2
Last updated on Jul 22, 2025
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