Homework Help

Show that  `25m^2-40mn+16n^2` is non-negative for all values of m and n.

user profile pic

parama9000 | TA , Grade 11 | Valedictorian

Posted April 16, 2013 at 9:46 AM via web

dislike 2 like

Show that  `25m^2-40mn+16n^2` is non-negative for all values of m and n.

2 Answers | Add Yours

user profile pic

Mary Joy Ripalda | High School Teacher | (Level 3) Educator

Posted April 16, 2013 at 10:14 AM (Answer #1)

dislike 2 like

To prove that `25m^2-40mn +16n^2` is non-negative for all values of m and n, set the polynomial greater than and equal to zero.

`25m^2-40mn +16n^2gt=0`

Then, factor.

`(5m-4n)(5m-4n)gt=0`

`(5m-4n)^2gt=0`

Then, consider this property of exponent which is:

`x^ngt=0 `   when n is an even number.

Since the exponent of the factor `5m-4n` is 2 which is an evennumber, then the inequality equation `(5m - 4n)^2gt=0` is always true.

Hence,  `25m^2-40mn +16n^2` is non-negative for any values of m and n.

user profile pic

oldnick | Valedictorian

Posted April 16, 2013 at 1:07 PM (Answer #2)

dislike 0 like

`25mn^2-40mn+16n^2=(5m-4n)^2>=0`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes