if,
$a+b+c=3$
$ab+bc+ca=3$
$abc=1$
Prove that $a=b=c=1$
3 variables
-
Thanic Nur Samin
- Posts:176
- Joined:Sun Dec 01, 2013 11:02 am
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Because destroying everything mindlessly isn't cool enough.
-
Phlembac Adib Hasan
- Posts:1016
- Joined:Tue Nov 22, 2011 7:49 pm
- Location:127.0.0.1
- Contact:
Re: 3 variables
Let $P(x)=(x-a)(x-b)(x-c)$
Using the given values, $P(x)=x^3-3x^2+3x-1\Longleftrightarrow P(x)=(x-1)^3$
Therefore, $1$ is the only root of $P(x)\Longleftrightarrow a=b=c=1$.
Using the given values, $P(x)=x^3-3x^2+3x-1\Longleftrightarrow P(x)=(x-1)^3$
Therefore, $1$ is the only root of $P(x)\Longleftrightarrow a=b=c=1$.
Welcome to BdMO Online Forum. Check out Forum Guides & Rules