Let a, b and c be positive numbers satisfying ab = 11.25; ac = 20; and bc = 36. What is the value of c?
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b=11.25/a (from first equation)
c=36/b = 36a/11.25
ac=20
a * [36a / 11.25] = 20
solve for a =15/6
c= 36a/11.25 = 36(15/6) /11.25 = 8
ab = 11.25 ⇒ b = 11.25 / a (1)
ac = 20 ⇒ c = 20 / a (2)
bc = 36 (3)
Sub (1) and (2) into (3)
(11.25 /a ) (20 / a) = 36
225/ a^2 = 36 rearrange as
a^2 = 225/36 take the positive root
a = 15 / 6 = 5 / 2
So....using (2).....
c = 20 / ( 5/2) = 8
Really cool! Thanks CPhill! Man Im glad I found this math site
What do you mean by positive root.
225 / 36 has two roots : (-15/6) and (15/6)
If we square both of these.....we get 225 /36
But.....since "a" is positive....we need 15 / 6 = 5 / 2
Does that make sense ???
Oh yea! I remember the 2 roots thing from quadratic equations but I didnt know that one was a minus number. I remember some them had two plus numbers. How do you know which one to use if they are both plus numbers?