Question

Sum of a number and its reciprocal is 25/12.Find the numbers?

Answer 1

check the attachment

Answer 2

Answer:

x = 4/3 , 3/4

Step-by-step explanation:

Let the number be x

Reciprocal of number = $\frac{1}{x}$

We are given that Sum of a number and its reciprocal is 25/12.

So, $x+\frac{1}{x}=\frac{25}{12}$

$\frac{x^2+1}{x}=\frac{25}{12}$

$12x^2+12=25x$

$12x^2-25x+12=0$

$12x^2-9x-16x+12=0$

$3x(4x-3)-4(4x-3)=0$

$(3x-4)(4x-3)=0$

So, x = 4/3 , 3/4

Thus the number can be  x = 4/3 , 3/4