Question
The following are quadratic equations in x?
$\text{x}^2-\frac{1}{\text{x}^2}=5$
$\text{x}^2-\frac{1}{\text{x}^2}=5$
✓
Answer
$\text{x}^2-\frac{1}{\text{x}^2}=5$
$\Rightarrow x^4- 1 = 5x^2$
$\Rightarrow x^4 - 5x^2 - 1 = 0$
And $(x^4 - 5x^2 - 1)$ Being a polynomial of degree $4$
$\therefore\ \text{x}^2-\frac{1}{\text{x}^2}=5$ is not a quadratic equation.
$\Rightarrow x^4- 1 = 5x^2$
$\Rightarrow x^4 - 5x^2 - 1 = 0$
And $(x^4 - 5x^2 - 1)$ Being a polynomial of degree $4$
$\therefore\ \text{x}^2-\frac{1}{\text{x}^2}=5$ is not a quadratic equation.
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