This turned out to be ridiculously easy:
My answer will be in the comments section.
Thursday, June 22, 2023
1 comment:
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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.