Question
Solve the following quadratic equation:$\frac{2}{\text{x}^2}-\frac{5}{\text{x}}+2=0$
✓
Answer
$\frac{2}{\text{x}^2}-\frac{5}{\text{x}}+2=0$ Multiplying by $x^22 - 5x + 2x^2 = 0$ or $2x^2 - 5x + 2 = 0$
$\Rightarrow 2x^2 - 4x - x + 2 = 0$
$\Rightarrow 2x(x - 2) - 1(x - 2) = 0$
$\Rightarrow (x - 2)(2x - 1) = 0$
$\therefore$ $x - 2 = 0$ or $2x - 1 = 0$
$⇒ x = 2$, $\text{x}=\frac{1}{2}$
Hence, $2$ and $\frac{1}{2}$ are the roots of the given equation.
$\Rightarrow 2x^2 - 4x - x + 2 = 0$
$\Rightarrow 2x(x - 2) - 1(x - 2) = 0$
$\Rightarrow (x - 2)(2x - 1) = 0$
$\therefore$ $x - 2 = 0$ or $2x - 1 = 0$
$⇒ x = 2$, $\text{x}=\frac{1}{2}$
Hence, $2$ and $\frac{1}{2}$ are the roots of the given equation.
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