A fraction is greater than its reciprocal by 9/20. What is the fraction? ?->(Show Answer!)

1. A fraction is greater than its reciprocal by 9/20. What is the fraction?

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By: anil on 05 May 2019 01.45 am

Let that fraction be $$frac{1}{x}$$ $$ (frac{1}{x}) = x + 9/20$$ $$Rightarrow 20x^{2}+9x-20 = 0$$ $$Rightarrow(x+frac{25}{20})(x-frac{16}{20})=0$$ $$Rightarrow(x+5/4)(x-4/5)=0$$ $$Rightarrow x = -5/4 or 4/5$$ $$Rightarrow ext{fraction} = frac{1}{x} = -4/5 ext(or) 5/4$$ so the answer is option A.

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