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| 1. |
The difference of two no. Is 4 if the difference of their reciprocal is 4/21 find the no. |
| Answer» Let first number be x.Then,\xa0second number = x + 4\xa0According to the question ,{tex}\\frac{1}{x} - \\frac{1}{x+4} =\\frac{4}{21}{/tex}{tex}\\begin{array}{l}\\frac{x\\;+\\;4\\;-\\;x\\;}{x(x+4)}=\\;\\;\\frac4{21}\\\\\\frac{\\;4}{x^2\\;+4\\;x}=\\;\\;\\frac4{21}\\\\4(x^2\\;+\\;4x)\\;=\\;84\\end{array}{/tex}⇒ 4x2 + 16x - 84 = 0⇒4(x2 +4 x - 21) = 0⇒ (x2 +4 x - 21) = 0⇒(x +7) (x -3) = 0⇒ x +7 = 0 or x - 3 = 0⇒ x = -7 or x = 3Therefore, the two numbers are 3 and 7 or -7 and -3 | |