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  • Find the roots of the following equations: (i) x - 1 / x = 3, x not equals 0

Q3.    Find the roots of the following equations:

                (i)    x - \frac{1}{x} = 3, x\neq 0

Answers (2)

best_answer

Given equation: x - \frac{1}{x} = 3, x\neq 0

So, simplifying it,

\Rightarrow \frac{x^2-1}{x} = 3

\Rightarrow x^2-3x-1 = 0

Comparing with the general form of the quadratic equation: ax^2+bx+c = 0, we get

a=1,\ b=-3,\ c=-1

Now, applying the quadratic formula to find the roots:

x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}

\Rightarrow x= \frac{3 \pm \sqrt{9+4}}{2}

\Rightarrow x= \frac{3 \pm \sqrt{13}}{2}

Therefore, the roots are

 \Rightarrow x = \frac{3+\sqrt{13}}{2}\ or\ \frac{3 - \sqrt{13}}{2}

 

 

 

Posted by

Divya Prakash Singh

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X-1/x=3,

X×X-1×|/x=3

X²-1=3x

X²-3x-1=0

Comparing with ax²+bx+c=0

a=1;b=-3;c=-1

-b±√b²-4ac/2a

-(-3)±√(-3)²-4(1)(-1)/2(1)

3±√9+4/2

3±√13/2

3±√13/2

 X=3+√13/2 or X =3-√13/2

Posted by

E.Akshitha

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