The sum of a non-zero number and its reciproc | vedclass

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Question

(B) Let the required non-zero number be $x$.Then,its reciprocal is $\frac{1}{x}$.According to the problem,their sum is $\frac{10}{3}$.So,$x + \frac{1}

Vedclass · Accepted Answer

$3$ and $\frac{1}{3}$

Vedclass · Answer

(B) Let the required non-zero number be $x$.Then,its reciprocal is $\frac{1}{x}$.According to the problem,their sum is $\frac{10}{3}$.So,$x + \frac{1}{x} = \frac{10}{3}$.Multiplying the entire equation by $3x$,we get $3x^2 + 3 = 10x$.Rearranging the terms,we get the quadratic equation $3x^2 - 10x + 3 = 0$.Factoring the quadratic equation: $3x^2 - 9x - x + 3 = 0$.$3x(x - 3) - 1(x - 3) = 0$.$(3x - 1)(x - 3) = 0$.This gives $x = \frac{1}{3}$ or $x = 3$.If the number is $3$,its reciprocal is $\frac{1}{3}$. If the number is $\frac{1}{3}$,its reciprocal is $3$.Thus,the required numbers are $3$ and $\frac{1}{3}$.

The sum of a non-zero number and its reciprocal is $\frac{10}{3}$. Find the numbers.

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