Question

If the sum of a number and its reciprocal is 10/3 ,then number is
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Answer 1

Given:-

• The sum of a number and it's reciprocal is 10/3

To find:-

• The number

Answer:-

Let the number be x.

Then the reciprocal of the number will be 1/x

According to the question, the sum of the number (x) and it's reciprocal (1/x) is 10/3.

So, we can write an equation in x as follows,

$\sf \: x + \dfrac{1 }{x} = \dfrac{10}{3}$

$\sf \longrightarrow \dfrac{ {x}^{2} + 1 }{x} = \dfrac{10}{3}$

$\sf \longrightarrow3(x {}^{2} + 1) = 10x$

$\sf \longrightarrow3 {x}^{2} + 3 = 10x$

$\sf \longrightarrow3 {x}^{2} - 10x + 3 = 0$

$\sf \longrightarrow3x {}^{2} - 9x - x + 3 = 0$

$\sf \longrightarrow3x(x - 3) - 1(x - 3) = 0$

$\sf \longrightarrow(x - 3)(3x - 1) = 0$

If (x - 3) = 0,

$\sf \longrightarrow \underline{ \underline{ \sf{ \green{x = 3}}}}$

If (3x - 1) = 0,

$\sf \longrightarrow \underline{ \underline{ \sf{ \green{x = \dfrac{1}{3} }}}}$