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Solve the Following Quadratic Equations by Factorization: `1/X-1/(X-2)=3` , X ≠ 0, 2 - Mathematics

Solve the following quadratic equations by factorization:

`1/x-1/(x-2)=3` , x ≠ 0, 2

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Solution

We have been given

`1/x-1/(x-2)=3`

-2 = 3x2 - 6x

3x2 - 6x + 2 = 0

`3x^2 - (3 + sqrt3)x-(3-sqrt3)x+3-sqrt3+sqrt3-1=0`

`x(3x-3-sqrt3)+((-3+sqrt3)/3)(3x-3-sqrt3)=0`

`((3x-3+sqrt3)/3)(3x-3-sqrt3)=0`

`(sqrt3x-sqrt3+1)(sqrt3x-sqrt3-1)=0`

Therefore,

`sqrt3x-sqrt3+1=0`

`sqrt3x=sqrt3-1`

`x(sqrt3-1)/sqrt3`

or

`sqrt3x-sqrt3-1=0`

`sqrt3x=sqrt3+1`

`x(sqrt3+1)/sqrt3`

Hence, `x(sqrt3-1)/sqrt3` or `x(sqrt3+1)/sqrt3`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 4 Quadratic Equations
Exercise 4.3 | Q 12 | Page 19
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