Question
Solve the following quadratic equation:$\text{10x}-\frac{1}{\text{x}}=3$
✓
Answer
$\text{10x}-\frac{1}{\text{x}}=3$
$\Rightarrow 10x^2 - 1 = 3x$
$\Rightarrow 10x^2 - 5x + 2x + 1 = 0$
$\Rightarrow 5x(2x - 1) + 1(2x - 1) = 0$
$\Rightarrow (5x + 1)(2x - 1) = 0$
$\Rightarrow (5x + 1)(2x - 1) = 0$
$\Rightarrow 5x + 1 = 0 or 2x - 1 = 0$
$\Rightarrow\text{x}=\frac{-1}{5}$ or $\text{x}=\frac{1}{2}$
Hence, $\frac{-1}{5}$ and $\frac{1}{2}$ are the roots of the given equation.
$\Rightarrow 10x^2 - 1 = 3x$
$\Rightarrow 10x^2 - 5x + 2x + 1 = 0$
$\Rightarrow 5x(2x - 1) + 1(2x - 1) = 0$
$\Rightarrow (5x + 1)(2x - 1) = 0$
$\Rightarrow (5x + 1)(2x - 1) = 0$
$\Rightarrow 5x + 1 = 0 or 2x - 1 = 0$
$\Rightarrow\text{x}=\frac{-1}{5}$ or $\text{x}=\frac{1}{2}$
Hence, $\frac{-1}{5}$ and $\frac{1}{2}$ are the roots of the given equation.
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