Question

a,b is greater than 0. prove that a+b/2 is greater than or equal to√ab

answer it I will mark as brainlist​

Answer 1

Explanation:

I am reading a chapter about mathematical proofs. As an example there is: Prove that:

(1)           a+b2≥ab−−√(1)           a+b2≥ab

for a,b>0a,b>0. There is stated that the thesis for the proof is short multiplication formula:

(2)         (a+b)2=a2+2ab+b2(2)         (a+b)2=a2+2ab+b2

Substracting from the short multiplication (2)(2) formula 4ab4ab and using square root yields the proof by implication. (here ends the example in a book)

Please tell me if I am right about it:

we are considering only a,b∈R+a,b∈ℜ+

(1)(1) can be transformed into a−2ab−−√+b≥0a−2ab+b≥0 which is an equivalent short multiplication formula (x−y)2=x2−2xy+y2(x−y)2=x2−2xy+y2

taking into account assumptions squared number is always equal or greater than zero.

the aplication says that if squared number is greater than zero then (1) is true.please mark me as brilliant

Answer 2

Thanks for asking this question it is very helpful