If a ,b ,c are positive, then prove that...

If `a ,b ,c` are positive, then prove that `a//(b+c)+b//(c+a)+c//(a+b)geq3//2.`

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we have
`(a)/(b + c) + (b)/(c + a) + (c )/(a + b) ge (3)/(2)`
`implies (a)/(b + c) + 1 + (b)/(c + a) + 1 + (c )/(a + b) + 1 ge (3)/(2) + 3`
`implies (a + b + c)/(b + c) + (a + b + c)/(c + a) + (a + b+ c)/(a + b) ge (9)/(2)`
`(1)/(b + c) + (1)/(c + a) + (1)/(a + b) ge (9)/(2(a + b + c))`
Now, using A.M `ge` H.M we have
`((1)/(b + c) + (1)/(c + a) + (1)/(a + b))/(3) ge (3) ((a + b) + (b + c) + (c + a))`
`implies (1)/(b + c) + (1)/(c + a) + (1)/(a + b) ge (9)/(2(a + b + c))`

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