Question

The sum of a number and its reciprocal is 25/12. what are the two numbers

Answer 1

Two numbers are 4/3 or 3/4

Answer 2

Answer:

$\frac{4}{3},\frac{3}{4}$

Step-by-step explanation:

Let the number be x

Reciprocal = 1/x

Since we are given that sum of a number and its reciprocal is 25/12.

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

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

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

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

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

$x=\frac{4}{3},\frac{3}{4}$

Thus the numbers are $\frac{4}{3},\frac{3}{4}$