Which of the following are quadratic equations?

$x^2\ +\ \frac{1}{x^2}\ =\ 5$

Given:

Given quadratic equation is $x^2\ +\ \frac{1}{x^2}\ =\ 5$.

To do:

We have to check whether the given equation is quadratic.

Solution:

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

$x^2\ +\ \frac{1}{x^2}\ =\ 5$

 $x^2 +\frac{1}{x^2} = 5$ can be written as,

$x^2(x^2)+x^2(\frac{1}{x^2}) = x^2(5)$  (Multiply by $x^2$ on both sides)

$x^4+1=5x^2$

$x^4-5x^2+1=0$

The equation $x^4-5x^2+1=0$ is not of the form $ax^2+bx+c=0$ as its degree is $4$.

Therefore, $x^2\ +\ \frac{1}{x^2}\ =\ 5$ is not a quadratic equation.

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Updated on: 10-Oct-2022

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