Solution to Show that for any positive number a and b, (a + b)/2 ≥ √ab - Sikademy
Author Image

Archangel Macsika

Show that for any positive number a and b, (a + b)/2 ≥ √ab

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

Solution

Proof.

(a + b)/2 ≥ √ab

(a + b)/2 ≥ √ab ⟺ ((a + b)/2)2 ≥ ab

⟺ (a + b)2 = 4ab

⟺ a2 + b2 + 2ab ≥ 4ab

⟺ a2 − 2ab + b2 ≥ 0

⟺ (a − b)2 ≥ 0

Since square on any number is greater than zero, so the (a − b)2 ≥ 0 and so we have the inequality.



Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-61-qpid-19