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Which of the following are quadratic equations?
$x\ +\ \frac{1}{x}\ =\ 1$
Given:
Given equation is $x\ +\ \frac{1}{x}\ =\ 1$.
To do:
We have to check whether the given equation is quadratic.
Solution:
The standard form of a quadratic equation is $ax^2+bx+c=0$.
$x\ +\ \frac{1}{x}\ =\ 1$
$x\ +\ \frac{1}{x}\ =\ 1$ can be written as,
$x(x)+x(\frac{1}{x})=x(1)$ (Multiply by $x$ on both sides)
$x^2+1=x$
$x^2-x+1=0$
$x^2-x+1=0$ is of the form $ax^2+bx+c=0$ where $a=1, b=-1$ and $c=1$.
Therefore, $x\ +\ \frac{1}{x}\ =\ 1$ is a quadratic equation.
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