Thursday, June 22, 2023

figure it out

This turned out to be ridiculously easy:

My answer will be in the comments section.



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Posted by Kevin Kim at 6/22/2023 11:14:00 PM

1 comment:

Kevin Kim said...

We're supposed to solve the following:

1/(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.

June 22, 2023 at 11:23:00 PM GMT+9

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