Question

The sum of a number and its reciprocal is
13
Find the number.
.
6




this right​

Answer 1

Answer

Yes , It is right

Step-by-step explanation:

Answer 2

Question:-

The sum of a number and it's reciprocal is $\frac{13}{6}$

Find the number

Solution:-

Let the number be x

The reciprocal will be $\frac{1}{x}$

Given,

The sum of two numbers is 13/6

So,$x + \frac{1}{x} = \frac{13}{6}$

$\frac{ {x}^{2} + 1 }{x} = \frac{13}{6}$

Cross multiply

$6( {x}^{2} + 1) = 13( x)$

$6 {x}^{2} + 6 = 13x$

$6 {x}^{2} - 13x + 6 = 0$

6×6 = 36

36 can be written as 9×4

So,

$6 {x}^{2} - 9x - 4x + 6 = 0$

$3x(2x - 3) + 2(2x - 3)$

$(2x - 3)(3x + 2)$

$2x - 3 = 0 \: \: \: and \: \: 3x + 2 = 0$

$x = \frac{3}{2} \: \: or \: \: x = - \frac{2}{3}$

The number is maybe 3/2 or -2/3