Question
Sat October 27, 2012 By:

Find the roots of the equation 1/2x-3 + 1/x-5 = 1

Expert Reply
Sat October 27, 2012

Answer : to find the roots of given equation :

[1/(2x-3) ] + [1/ (x-5)] = 1

=> x-5+2x-3 = (2x-3)(x-5) {taking the LCM and multiplying the denomenator on RHS}

=> 2x2-16x+23 = 0

it is a quadratic equation where a = 2 , b =-16 , c = 23

D = b2 - 4ac
    = (-16)2 - 4 (2)(23)
    = 256 -  184
     = 72
    = k2 + 16
 
x = (-b + D1/2 ) / 2a and x = (-b - D1/2 ) / 2a
=> x = (16 + 721/2) / 4 and (16 - 721/2) / 4
=> x = [16 + 6 (21/2) ] /4 and [16 - 6 (21/2) ] /4 
=> x = [8 + 3 (21/2) ] /2 and [8 - 3 (21/2) ] /2 Answer
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