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Quadratic Equation — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsQuadratic Equation4 Marks
Question
Solve the equation $2 x -\frac{1}{x}=7$. Write your answer correct to two decimal places.
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Answer

Solve the equation $2 x-\frac{1}{x}=7$
$2 x^2-1=7 x $
$ 2 x^2-7 x-1=0$
For quadratic equation $a x^2+b x+c=0$
$x =\frac{-b \pm \sqrt{2^2-4 a c}}{2 a}$
Here, $a =2, b =-7, c =-1$
Therefore,
$x=\frac{-(-7) \pm \sqrt{(-7)^2-4 \times 2 \times(-1)}}{2 \times 2} $
$x=\frac{7 \pm \sqrt{49+8}}{4} $
$=\frac{7 \pm \sqrt{57}}{4}$
$=\frac{7+\sqrt{57}}{4} \text { or } x=\frac{7-\sqrt{57}}{4} $
$ x=\frac{7+7 \cdot 550}{4} \text { or } x=\frac{7-7 \cdot 550}{4}$
$x = 3.64$ or $x = -0.14$

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