If xy = 144, x + y = 30, and x > y, what is the value of x – y ?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the equations:

x*y = 144.............(1)

x+ y= 30 .............(2)

We will use the substitution method to find the values of x and y.

from (2) we know that y= 30-x

Now we will substitute into (1).

==> x*y= 144

==> x*(30-x) = 144

Now we will open the brackets.

==> 30x - x^2 = 144

==> x^2 - 30x + 144 = 0

Now we will factor.

==> (x -24) ( x-6)  = 0

==> x1= 24 ==> y1= 30-24 =6

==> x2= 6==> y2= 30-6 = 24

But we know that x>y

Then the values are : x= 24 and y= 6

Now we need to find the values of x-y

==> x-y = 24-6 = 18

 

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have xy = 144, x + y = 30, and x > y, we need to find x - y.

x - y = sqrt ( x - y)^2 = sqrt [ (x + y)^2 - 4xy]

=> sqrt [ 30^2 - 4* 144]

=> sqrt [ 900 - 576]

=> sqrt (324)

=> 18

Therefore x - y = 18

haneeaaa's profile pic

haneeaaa | Student | eNotes Newbie

Posted on

24 x 6=144

24+6=30

24>6=30   x=24

24-6=18

ur anwer is 18

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