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Find the Roots of the Equation . 1 2 X − 3 + 1 X + 5 = 1 , X ≠ 3 2 , 5 - Mathematics

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Find the roots of the equation  .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`

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Solution

`1/(2x-3)+1/(x+5)=1`

`rArr ((x-5)+(2x-3))/((2x-3)(x-5))=1`

`rArr 3x-8=(2x-3)(x-5)`

`rArr 3x-8=2x^2-10x-3x+15`

`rArr 3x-8=2x^2-13x+15`

`rArr 2x^2-16x+23=0`

`∴ x=(-(-16)+-sqrt(-16)^2-4xx2xx23)/(2xx2)`

`=(16+-sqrt256-184)/4`

`=(16+-sqrt2)/4`

`=(16+-6sqrt2)/4`

`=(2(8+-3sqrt2))/4`

`=1/2(8+3sqrt2) or ` `1/2(8-3sqrt2)`

`∴x=1/2(x+3sqrt2)or1/2(8-3sqrt2)`

Concept: Nature of Roots
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