Question

A natural number, when increased by 12, equal 160 times its reciprocal. We would
like to find the number

Answer 1

Answer

Hence, the required natural number is 8.

explain

$x + 12 = \frac{160}{x} \\ = > {x}^{2} + 12x - 160 = 0 \\ \\ \\ = > x(x \times20) - 8(x + 20) = 0 \\ = > x = - 20(not \: possible) or \: x = 8 \\ = > {x}^{2} 20x - 8x - 160 = 0 \\ (x + 20)( x + 20)(x - 8) = 0$

Answer 2

Hence, the required natural number is 8.

explain

\begin{gathered}x + 12 = \frac{160}{x} \\ = > {x}^{2} + 12x - 160 = 0 \\ \\ \\ = > x(x \times20) - 8(x + 20) = 0 \\ = > x = - 20(not \: possible) or \: x = 8 \\ = > {x}^{2} 20x - 8x - 160 = 0 \\ (x + 20)( x + 20)(x - 8) = 0\end{gathered}

x+12=

x

160

=>x

2

+12x−160=0

=>x(x×20)−8(x+20)=0

=>x=−20(notpossible)orx=8

=>x

2

20x−8x−160=0

(x+20)(x+20)(x−8)=0