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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Updated on: 10-Oct-2022

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