If j, k, and l are positive with jk = 24, jl = 48, and kl = 18, find j + k + l.
If j, k, and l are positive with jk = 24, jl = 48, and kl = 18, find j + k + l.
jk = 24 ⇒ 24/j = k
jl = 48 ⇒ 48/j = l
kl = 18
So
kl = 18
(24/j) (48/j) = 18
1152 / j^2 = 18
j^2 = 1152/18
j^2 = 64 take the positive root
j = 8
So.....24 / j = k ⇒ 24 / 8 = k ...... 3 = k
And 48 / j = l ⇒ 48 / 8 = l ...... 6 = l
So
j + k + l = 8 + 3 + 6 = 17