Question

State whether $x+\frac{1}{x^2}=3$ is a quadratic equation.

Answer 1

Step 1: Definition of a quadratic equation

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

For a given equation to be a quadratic equation, $a\ne 0$ and the highest power of the variable in the equation should be $2$.

Step 2: To check whether the equation is a quadratic equation

Writing the given equation $x+\frac{1}{x^2}=3$ in standard form.

$$\begin{gathered} x+\frac{1}{x^2}=3 \\ \Rightarrow x^3+1=3x^2 \\ \Rightarrow x^3-3x^2+1=0 \end{gathered}$$

On comparing this equation with the standard form $a{x}^2+bx+c=0$, we can see that $a=-3$.

However, the highest power of the variable $x$ is $3$.

Hence, the equation $x+\frac{1}{x^2}=3$ is not a quadratic equation.