Question

If the sum of natural no. and its reciprocal is 10/3 find the no.
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Answer 1

Step-by-step explanation:

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Answer 2

$\large\boxed{\fcolorbox{blue}{yellow} {Answer}}$

The natural no. is 3.

$\large\boxed{\fcolorbox{blue}{yellow} {Step - by - step explanation }}$

Given

The sum of a natural no. and its reciprocal is 10/3.

To find

The natural no.

Solution

Let the natural no. be x.

And its reciprocal be 1/x.

From the given condition,

$x + \frac{1}{x} = \frac{10}{3} \: \: .....(1)$

By multiplying each term in equation (1) by x, we get,

$x + \frac{1}{x} = \frac{10}{3} \\ \\ {x}^{2} + 1 = \frac{10x}{3} \\ \\ 3( {x}^{2} + 1) = 10x \\ 3 {x}^{2} + 3 = 10x \\ 3 {x}^{2} + 3 - 10x = 0 \\ 3 {x}^{2} - 10x + 3 = 0 \\ \\ 3 {x}^{2} - 9x - x + 3 = 0 \\ 3x(x - 3) - 1(x - 3) = 0 \\ (x - 3)(3x - 1) = 0 \\ \\ (x - 3) = 0 \\ x - 3 = 0 \\ x = 3 \\ \\ now \\ (3x - 1) = 0 \\ 3x - 1 = 0 \\ 3x = 1 \\ x = \frac{1}{3}$

But, we have given that the number is a natural no. So, x = 1/3 is unacceptable.

.°. x = 3

Ans. :

The natural number is 3.

Hope it helps!

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