Question

the difference between a positive proper fraction and it's reciporcal is 9/20 find the fraction
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Answer 1

Answer:

x=4/5

Step-by-step explanation:

Let the fraction be x.

∴ 1/x-x = 9/20

Taking LCM, we get

(1-x²)/x = 9/20

20(1-x²) = 9x

20-20x² = 9x

20x²+9x-20=0

Splitting the middle term

20x²+25x-16x-20=0

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

∴ (4x+5)(5x-4)=0

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

∴ x= -5/4 OR x=4/5

Since we need a positive fraction, we will take  x=4/5

x/y - y/x = 9/20

Taking LCM

(x² - y²)/xy = 9/20

20(x² - y²)= 9xy