If a(square)2 + 2b = 7, b2 + 4c = -7 and c2 + 6a = -14, then what is the value of a2 + b2 + c2

Asked by Kaushik Gambhir | 25th Jul, 2010, 12:00: AM

Expert Answer:

Adding all the three equations we get,
a2 + b2 + c2 = 7 - 2b - 7 - 4c - 14 - 6a
a2 + b2 + c2 =  - 2b  - 4c - 14 - 6a
a2 + b2 + c2 =   - 14 - 2(3a + b + 2c)
Since LHS will always be positive (3a + b + 2c) must be negative and should be greater than 14 when multiplied by 2.
By inspection we find a = -3, b = -1 and c = -2.
So that
a2 + b2 + c2 = 14
- 14 - 2(3a + b + 2c) = 14
Hence,
a2 + b2 + c2 = 14
Regards,
Team,
TopperLearning.

Answered by  | 26th Jul, 2010, 11:43: AM

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