the denominator of a fraction is 2 more than the numerator. if sum of the fraction and its reciprocal is 34/ 15, find the fraction.
Answers
Answered by
8
let numerator be x
then denominator be x+2
a.t.q.
x/x+2+x+2/x=34/15
x^2+x^2+2x+2x+4/x^2+2x=34/15
2x^2+4x+4/x^2+2x=34/15
30x^2+60x+60=34x^2+68x
4x^2+8x-60=0
x^2+2x-15=0
on solving these equation
we will get two values of x
(x+5)(x-3)
x=-5 then fraction is -5/3
x=3 then fraction is 3/5
I hope it help u
then denominator be x+2
a.t.q.
x/x+2+x+2/x=34/15
x^2+x^2+2x+2x+4/x^2+2x=34/15
2x^2+4x+4/x^2+2x=34/15
30x^2+60x+60=34x^2+68x
4x^2+8x-60=0
x^2+2x-15=0
on solving these equation
we will get two values of x
(x+5)(x-3)
x=-5 then fraction is -5/3
x=3 then fraction is 3/5
I hope it help u
Similar questions