Question

The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:

Answer 1

Let x be the required fraction then acc to Q we have, 1/x - x = 9/20

So, (1-x^2)/x = 9/20

20 - 20x^2 =9x

20x^2 + 9x - 20 = 0

20x^2 - 25x-16x - 20 = 0

5x(4x+5)-4(4x+5) = 0

(5x-4) (4x+5) = 0

 Hence,x = 4/5

Answer 2

Given:

The difference between a positive proper fraction and its reciprocal is 9/20.

To Find:

The value of the fraction

Solution:

A fraction is a way to express parts of a thing by the whole of the same thing. They are expressed as p/q form. A proper fraction is a fraction in which the numerator is less than the denominator.

Let the proper fraction in the given question be x, so we can frame an equation for the condition as,

$\frac{1}{x} -x=\frac{9}{20}$

Now solving this equation to find the value of x, we have

[tex]\frac{1}{x} -x=\frac{9}{20} \\ 20(1-x^2)=9x\\ 20x^2+9x-20=0\\ 20x^2+25x-16x-20=0\\ 5x(4x+5)-4(4x+5)=0\\ (4x+5)(5x-4)=0\\ [/tex]

As the proper fraction is positive, then the value will be,

[tex]5x-4=0\\ x=\frac{4}{5} [/tex]

Hence, the positive proper fraction is 4/5.