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प्रश्न
Solve the following quadratic equations by factorization:
`(2x)/(x-4)+(2x-5)/(x-3)=25/3`
उत्तर
We have been given
`(2x)/(x-4)+(2x-5)/(x-3)=25/3`
`(2x(x-3)+(2x-5)(x-4))/(x^2-7x+12)=25/3`
6x2 - 18x + 6x2 - 24x - 15x + 60 = 25x2 - 175x + 300
13x2 - 118x + 240 = 0
13x2 - 78x - 40x + 240 = 0
13x(x - 6) - 40(x - 6) = 0
(x - 6)(13x - 40) = 0
Therefore,
x - 6 = 0
x = 6
or,
13x - 40 = 0
13x = 40
x = 40/13
Hence, x = 6 or x = 40/13
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