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If a+2b+3c=4, then find the least value ...

If `a+2b+3c=4,` then find the least value of `a^2+b^2+c^2dot`

A

`-2`

B

`2`

C

`8`

D

`-14`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `ab+bc+ca=((a+b+c)^(2)-(a^(2)+b^(2)+c^(2)))/(2)=183`
Hence `a`, `b`, `c` are the roots of the equation.
`t^(3)-24t^(2)+183t-440=0`
`implies(t-5)(t-8)(t-11)=0`
Thus `{a,b,c}={5,8,11}`
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