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| 1. |
The sum of the number and its reciprocal is 2 ×1/30.find the number |
| Answer» Let the number be x and its reciprocal be {tex}{1 \\over x}{/tex}According to the question{tex}x + {1 \\over x} = 2{1 \\over 30}{/tex}{tex}\\implies {x^2 +1 \\over x} = {61 \\over 30}{/tex}{tex}\\implies{/tex}30x2 - 61 x+30 = 0{tex}\\implies{/tex}30 x2 - 36x - 25x + 30 =0{tex}\\implies{/tex}6x ( 5x -6) - 5 (5x -6) = 0{tex}\\implies{/tex}(6x - 5) (5x - 6) = 0Either 6x - 5 = 0 or 5x - 6 = 0{tex}\\implies x = {5 \\over 6}, {6 \\over 5}{/tex}Hence, the required number is {tex}{5 \\over 6} \\,or \\,{6 \\over5}{/tex} | |