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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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