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Homework Statement
Let a,b and c be lengths of sides in a triangle, show that
√(a+b-c)+√(a-b+c)+√(-a+b+c)≤√a+√b+√c
The Attempt at a Solution
With Ravi-transformation the expressions can be written as
√(2x)+√(2y)+√(2z)≤√(x+y)+√(y+z)+√(x+z).
Im stuck with this inequality. Can´t find a way to use any known inequalities such as AM-GM or the rearrangement inequality.