+0

# Hello

0
18
1
+36

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

#1
+36
+1

I finally managed to solve it!!

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