if,
$a+b+c=3$
$ab+bc+ca=3$
$abc=1$
Prove that $a=b=c=1$
3 variables
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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 $P(x)\Longleftrightarrow a=b=c=1$.
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