Question
Solve the equation $2 x-\frac{1}{x}=7$ Write your answer correct to two decimal places.
✓
Answer
$2 x-\frac{1}{x}=7$
$\Rightarrow \frac{2 x^2-1}{x}=7$
$ \Rightarrow 2 x^2-1=7 x$
$\Rightarrow 2 x^2-7 x-1=0$
Here $a = 2, b = -7$ and $c = -1$
$\therefore x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$
$=\frac{-(-7) \pm \sqrt{(-7)^2-4(2)(-1)}}{2(2)} $
$ =\frac{7 \pm \sqrt{57}}{4}=\frac{7 \pm 7.55}{4}$
$=\frac{7+7.55}{4}$ and $\frac{7-7.55}{4}=3.64$ and $-0.14$
$\Rightarrow \frac{2 x^2-1}{x}=7$
$ \Rightarrow 2 x^2-1=7 x$
$\Rightarrow 2 x^2-7 x-1=0$
Here $a = 2, b = -7$ and $c = -1$
$\therefore x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$
$=\frac{-(-7) \pm \sqrt{(-7)^2-4(2)(-1)}}{2(2)} $
$ =\frac{7 \pm \sqrt{57}}{4}=\frac{7 \pm 7.55}{4}$
$=\frac{7+7.55}{4}$ and $\frac{7-7.55}{4}=3.64$ and $-0.14$
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