SOLUTION: Given 144/(2R) = (1/a^2) + (1/b^2) + (1/c^2), solve for R.

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Question 1208462: Given 144/(2R) = (1/a^2) + (1/b^2) + (1/c^2), solve for R.
Found 4 solutions by ikleyn, Edwin McCravy, AnlytcPhil, math_tutor2020:
Answer by ikleyn(52834)   (Show Source):
You can put this solution on YOUR website!
.
Given 144/(2R) = (1/a^2) + (1/b^2) + (1/c^2), solve for R.
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This problem assumes that you have 1 millimeter standard skills of simplifying fractions.

Given = + + is the same as = + + = + + = = . From here, we get R = . ANSWER

Solved.

Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website!
Ikleyn's solution above is correct.

Answer by AnlytcPhil(1807)   (Show Source):
You can put this solution on YOUR website!

Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!

Multiply both sides by the LCD a^2*b^2*c^2*R to clear out the fractions.

Distribute through a^2*b^2*c^2 on the right hand side. Do not distribute the R since we want to isolate it eventually.

Verification using WolframAlpha
https://www.wolframalpha.com/input?i=144%2F%282R%29+%3D+%281%2Fa%5E2%29+%2B+%281%2Fb%5E2%29+%2B+%281%2Fc%5E2%29%2C+solve+for+R
WolframAlpha decided to factor a^2 from a^2c^2 + a^2b^2.
The order of the terms being multiplied doesn't matter (eg: a^2b^2c^2 is the same as b^2a^2c^2), and neither does the order of the terms being added (eg: b^2c^2 + a^2c^2 is the same as a^2c^2+b^2c^2)

Another verification tool you can use is the CAS mode in GeoGebra.
There are many other tools to pick from.

Edit:
A way to avoid writing so many exponents, we can say