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For any real a, b, c the expression 2a^(...

For any real `a, b, c` the expression `2a^(2) + 11b^(2) + 4c^(2) - 8ab - 6bc - 2c + 41` is minimum then

A

`a - b - c = 0`

B

`a = 2b`

C

`a + b + c = 4`

D

`c = a`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`2(a^(2) + 4b^(2) - 4ab) + 3 (b^(2) + c^(3) - 2bc) + (c^(2) - 2c +1) + 40`
`2(a - 2b)^(2) + 3(b - c)^(2) + (c + 1)^(2) + 40`
min when `c = 1, b = 1, a = 2`
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