Question

the sum of three times a natural number and twice its reciprocal is 25/2. Find the number​

Answer 1

SOLUTION

GIVEN

The sum of three times a natural number and twice its reciprocal is 25/2

TO DETERMINE

The number

EVALUATION

Let the required natural number = x

Thrice the natural number = 3x

Twice the reciprocal of the number

$\displaystyle \sf{ = \frac{2}{x} }$

So by the given condition

$\displaystyle \sf{ 3x + \frac{2}{x} = \frac{25}{2} }$

$\displaystyle \sf{ \implies \frac{3 {x}^{2} + 2}{x} = \frac{25}{2} }$

$\displaystyle \sf{ \implies 6 {x}^{2} + 4 = 25x }$

$\displaystyle \sf{ \implies 6 {x}^{2} - 25x + 4 = 0 }$

$\displaystyle \sf{ \implies 6 {x}^{2} - 24x - x+ 4 = 0 }$

$\displaystyle \sf{ \implies 6x(x - 4) -1 (x - 4) = 0 }$

$\displaystyle \sf{ \implies (x - 4) (6x - 1) = 0 }$

$\displaystyle \sf{ \implies x = 4 \: , \: \frac{1}{6} }$

Since x is a natural number

$\displaystyle \sf{ \therefore \: \: x \ne \frac{1}{6} }$

$\displaystyle \sf{ \therefore \: \: x = 4}$

Hence the required natural number = 4

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