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\xa0the sum of intiger and their reciprocal is 145/12. Find the intiger ? |
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Answer» Solution:Let the integer = xThen reciprocal = 1/xAccording to Questionx + 1/x = 145/12=> (x2+1)/x = 145/12=> 12x2 + 12 = 145x=> 12x2\xa0- 145x + 12 = 0=> 12x2- 144x - x + 12 = 0=> 12x(x - 12) - 1(x - 12) = 0=> (x - 12)(12x - 1) = 0=> x = 12 and x = 1/12as X is integer x can\'t be 1/12Therefore the required integer is 12 Let the integer be x.x + 1/x = 145/1212x2\xa0- 145x + 12 = 012x2\xa0- 144x - x + 12 = 012x(x - 12) - 1(x - 12) = 0(x - 12)(12x - 1) = 0x = 12 and x = 1/12Therefore the required integer is 12. |
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