I know how to find the conjugate for 2 variable expressions, but I am right now trying to find the conjugate of a 3 variable expression (I'm talking about radical expressions, by the way).


I tried expanding \((a+b+c)(a-b-c)\) and hoped to find something along the format of \(a^2 \pm b^2\pm c^2\), but I didn't get that expression. 


Every time I multiply something along the lines of \((a+b+c)(a-b+c), (a+b+c)(-a+b+c), (a+b+c)(a+b-c)\), I always get a \(2ab,2ac\) or \(2bc\). I'm still stuck on this.


Also, can the website impliment a LaTeX using the same text as the question/answer? Thanks.

 Jan 6, 2024

I finally managed to solve it!!

(Thanks to my dad)


The question I was answering was:


\((\sqrt5+\sqrt3-\sqrt2)(3 \sqrt a -\sqrt b+2 \sqrt c)=12 \)


Find the ordered pair \((a,b,c)\).


I am planning on putting the solution on another post, though.


However, the clue is that \(5=3+2\), which makes this possible.



I wil post the solution on this question If I can't post it on the other post.

 Jan 6, 2024

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