The sum of a natural number and its reciproca | vedclass

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Question

(B) Let the natural number be $x$.According to the problem,the sum of the number and its reciprocal is $\frac{5}{2}$.So,$x + \frac{1}{x} = \frac{5}{2}

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Let the natural number be $x$.According to the problem,the sum of the number and its reciprocal is $\frac{5}{2}$.So,$x + \frac{1}{x} = \frac{5}{2}$.Multiplying the entire equation by $2x$ to clear the denominators,we get:$2x^2 + 2 = 5x$.Rearranging the terms to form a quadratic equation:$2x^2 - 5x + 2 = 0$.Factoring the quadratic equation:$2x^2 - 4x - x + 2 = 0$.$2x(x - 2) - 1(x - 2) = 0$.$(2x - 1)(x - 2) = 0$.This gives two possible values for $x$:$2x - 1 = 0 \implies x = \frac{1}{2}$ (not a natural number).$x - 2 = 0 \implies x = 2$ (a natural number).Therefore,the required natural number is $2$.

The sum of a natural number and its reciprocal is $\frac{5}{2}$. Then the number is $\ldots \ldots .$

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