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Solve the Following Quadratic Equations by Factorization: `(X-1)/(X-2)+(X-3)/(X-4)=3 1/3`, X ≠ 2, 4 - CBSE Class 10 - Mathematics

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Question

Solve the following quadratic equations by factorization:

`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`, x ≠ 2, 4

Solution

We have been given

`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`

3(x2 - 5x + 4 + x2 - 5x + 6) = 10(x2 - 6x + 8)

4x2 - 30x + 50 = 0

2x2 - 15x + 25 = 0

2x2 - 10x - 5x + 25 = 0

2x(x - 5) - 5(x - 5) = 0

(2x - 5)(x - 5) = 0

Therefore,

2x - 5 = 0

2x = 5

x = 5/2

or,

x - 5 = 0

x = 5

Hence, x = 5/2 or x = 5

  Is there an error in this question or solution?

APPEARS IN

Solution Solve the Following Quadratic Equations by Factorization: `(X-1)/(X-2)+(X-3)/(X-4)=3 1/3`, X ≠ 2, 4 Concept: Solutions of Quadratic Equations by Factorization.
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