- #1
Rectifier
Gold Member
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The problem
I want to solve the following inequality:
$$ x+\frac{1}{x}<1 $$
The attempt
## x+\frac{1}{x}<1 \\ x+\frac{1}{x}-1<0 \\ \frac{x^2}{x}+\frac{1}{x}-\frac{x}{x}<0 \\ \frac{x^2-x+1}{x}<0 ## ## x \neq 0 ##
I tried to factor the numerator to examine the polynomial with a character table but it has complex roots.
I want to solve the following inequality:
$$ x+\frac{1}{x}<1 $$
The attempt
## x+\frac{1}{x}<1 \\ x+\frac{1}{x}-1<0 \\ \frac{x^2}{x}+\frac{1}{x}-\frac{x}{x}<0 \\ \frac{x^2-x+1}{x}<0 ## ## x \neq 0 ##
I tried to factor the numerator to examine the polynomial with a character table but it has complex roots.