The sum of a number and its reciprocal is 10/3.Find the number.
The sum of a number and its reciprocal is 10/3.find the number
The sum of a number and its reciprocal is 10/3.find the number
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let the no. is\xa0{tex}x{/tex}reciprocal of\xa0{tex}x is \\frac1x{/tex}A.T.Q.{tex}x + \\frac1x=\\frac{10}3{/tex}{tex}\\implies{(x^2+1)\\over x}={10 \\over 3}{/tex}{tex}\\implies 3x^2+3=10x{/tex}{tex}\\implies 3x^2-10x+3=0{/tex}{tex}\\implies 3x^2-9x-x+3=0{/tex}{tex}\\implies 3x(x-3)-1(x-3)=0{/tex}{tex}\\implies (x-3)(3x-1)=0{/tex}{tex}\\implies x=3 \\;or\\;{1\\over3}{/tex}\xa0