a+b+c=(abc)^(1/2) show that (a(b+c))^(1/2)+(b(c+a))^(1/2)+(c(a+b))^(1/2)>36

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Expert Solution

Assuming (which should be given in the question as we are taking the square root of these numbers in the question).

For , by Arithmetic mean greater than or equal to geometric mean, we have

Since

we get

(This we are going to use in the last step of the question)

Now let us simplify .

By Arithmetic mean greater than or equal to geometric mean, we have . Thus,

Similarly, we have

and

Thus,

Again applying arithmetic mean greater than or equal to geometric mean, we have

Thus,

Colby Messinger answered 1 year ago

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