The difference of 2 numbers is 4 and difference of their reciprocals i

1.	The difference of 2 numbers is 4 and difference of their reciprocals is 4/2. Find the numbers
Answer» Let the two numbers be x and x – 4.Given that the difference of two numbers is 4.By the given hypothesis, we have\xa0{tex}\\frac{1}{x-4}-\\frac{1}{x}=\\frac{4}{21}{/tex}{tex}\\Rightarrow \\frac{x-x+4}{x(x-4)}=\\frac{4}{21}{/tex}{tex}\\Rightarrow 84 = 4x(x-4){/tex}{tex}\\Rightarrow x^2 - 4x -21=0{/tex}{tex}\\Rightarrow x^2 -7x+3x-21{/tex}{tex}\\Rightarrow (x-7)(x+3) = 0{/tex}{tex}\\Rightarrow x=7 \\ or\\ x=-3{/tex}If x = 7, then\xa0{tex}x-4=7-4=3{/tex}If\xa0x = -3, then\xa0{tex}x-4=-3-4=-7{/tex}Hence, required numbers are 3,7 and -3,-7

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