Which of the following are quadratic equations?

$x\ +\ \frac{1}{x}\ =\ x^2,\ x\ ≠\ 0$

Given:

Given equation is $x\ +\ \frac{1}{x}\ =\ x^2,\ x\ ≠\ 0$.

To do:

We have to check whether the given equation is quadratic.

Solution:

The standard form of a quadratic equation is $ax^2+bx+c=0$.

$x\ +\ \frac{1}{x}\ =\ x^2,\ x\ ≠\ 0$

$x(x)+x(\frac{1}{x})=x(x^2)$    (Multiply by $x$ on both sides)

$x^2+1=x^3$

$x^3-x^2-1=0$

The equation $x\ +\ \frac{1}{x}\ =\ x^2,\ x\ ≠\ 0$ is not of the form $ax^2+bx+c=0$ as its degree is $3$.

Therefore, $x\ +\ \frac{1}{x}\ =\ x^2,\ x\ ≠\ 0$ is not a quadratic equation.

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Updated on: 10-Oct-2022

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