Question

In: Advanced Math

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

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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