The denominator of a fraction is two more than it's numerator.if the sum of the fraction and it's reciprocal is 34/15,find the fraction
Answers
Solution :
In the above question, it is given that for a fraction , the denominator is 2 more than the numerator.
Let us assume that the numerator of the fraction being discussed here is x.
So, the denominator of the fraction becomes :
> ( x + 2 )
By now, we already have an idea about the fraction ;
> ( x )/(x + 2)
Its reciprocal becomes just the opposite ;
> (x+2)/x
The sum of the fraction and its reciprocal is 34/15
> x/x+2 + (x+2)/x = 34/15
> Taking LCM
> x(x+2) + (x+2)^2/x(x+2) = 34/15
> x^2 + 2x + x^2 + 4x + 4/x(x+2) = 34/15
> 2x^2 + 6x + 4/x(x+2) = 34/15
> 2( x^2 + 3x + 4)/x(x+2) = 34/15
> 30( x^2 + 3x + 4) = 34( x^2 + 2x)
> 15(x^2 + 3x + 4) = 17(x^2 + 2x)
> 30x^2 + 45x + 60 = 17x^2 +34x
> 13x^2 + 9x + 60 = 0
> This has no real solution as D < 0 .
The data in the question is wrong.
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