Question

What is the conjugate?

x- √2

Answer 1

\(x + \sqrt 2\)

Answer 2

For \(\large\color{blue}{ \displaystyle a+b }\), the conjugate is \(\large\color{royalblue}{ \displaystyle a-b }\). For \(\large\color{brown}{ \displaystyle a-b }\), the conjugate is \(\large\color{orangered}{ \displaystyle a+b }\)

Answer 3

It just has to be that when you multiply something times its conjugate, that you get something that looks like
\(\large\color{black}{ \displaystyle (a+b)(a-b) }\)

Answer 4

which then simplifies to: \(\large\color{black}{ \displaystyle (a+b)(a-b)=a^2-b^2 }\)

Answer 5

Yes, for \(\color{black}{ \displaystyle x-\sqrt{2} }\) , it is \(\color{black}{ \displaystyle x+\sqrt{2} }\) .

Answer 6

@solomonzelman
Thank you very much for explaining !

Answer 7

sure, yw!