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Tyro
Asked: 2021-03-30T02:59:13+00:00 In: ,

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The sum of a number and 12 times its reciprocal is 7. Find the number

 

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  2. acedstud

    Let the number be x, then the reciprocal is \dfrac{1}{x}. Thus, 12 times the reciprocal is 12\times\dfrac{1}{x}=\dfrac{12}{x}.

    Now, the sum of the number and 12 times its reciprocal is 7 means x+\dfrac{12}{x}=7.

    To remove the fraction, we multiply through by the denominator, x, to get x(x)+x\cdot\dfrac{12}{x}=x(7)\Rightarrow x^2+12=7x\Rightarrow x^2-7x+12=0.

    Factorizing the quadratic equation, where -3 and -4 are the factors of 12 which add up to -7, we have (x-3)(x-4)=0.

    \Rightarrow x-3=0 or x-4=0

    \Rightarrow x=3 or x=4.

    Therefore, the numbers are 3 and 4.

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