Using equation 9 x 2 </msup> + 8 x y + 7 y 2 </msup> =

babajijwerz

babajijwerz

Answered question

2022-05-28

Using equation 9 x 2 + 8 x y + 7 y 2 = 6 to find maximum possible value of 7 x + 5 y + 12 x y

Answer & Explanation

Austin Solis

Austin Solis

Beginner2022-05-29Added 12 answers

Given 6 = 7 x 2 + 5 y 2 + 2 ( x + y ) 2 + 4 x y
From AM-GM inequality, 7 x 2 + 7 4 7 x , 5 y 2 + 5 4 5 y , 2 ( x + y ) 2 8 x y
Adding the three inequalities with the first equality, we have 6 + 7 4 + 5 4 7 x + 5 y + 12 x y, and the maximum of 9 is when the AM-GMs all have equality, i.e. when x = y = 1 2

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?