1.

If a,b,c are three positive real numbers then the minimum value of (a+3c)/(a+2b+c)+(4b)/(a+b+3c)-(8c)/(a+b+3c) is alpha+betasqrt(2) (where a,b in Z), then |alpha+beta| is equal to_____

Answer»


Solution :Let `a+2b+c=x,a+b+2c=y,a+b+3c=z`
`a=-x+5y-3z,b=z+x-2, c-z-y`
APPLY A.M. `ge` G.M.
`(a+3c)/(a+2b+c)+(4b)/(a+b+2c)-(8C)/(a+b+3c) ge -17 + 12 sqrt(2)`


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