All comments are subject to approval before they are published, so they will not appear immediately. Comments should be civil, relevant, and substantive. Anonymous comments are not allowed and will be unceremoniously deleted. For more on my comments policy, please see this entry on my other blog.
We're supposed to solve the following:
ReplyDelete1/(a^2) + 1/(b^2) + 1/(c^2)
after we're given that
ab = 1/2
bc = 1/3
ac = 1/6
Without doing any fancy math (like in the video, which shows a preposterously complicated solution), you can easily see that
• ab is 3 times greater than ac
• bc is 2 times greater than ac
So one equation we can make right away is
b = 3c (because a is a constant)
Plug that into bc = 1/3, and you get
3c(c) = 1/3
c^2 = 1/9
c = 1/3
So if b = 3c, then
b = 1
And if you then solve for a, you get
a = 1/2
Plug all that into what we're supposed to solve, and you get
1/[(1/2)^2] = 4
1/[(1)^2] = 1
1/[(1/3)^2] = 9
4 + 1 + 9 = 14.
QED.