Question

The sum of a number and it's reciprocal is -25/12.find the number.

Answer 1

Hi friend!!

Let the number be x. Then it's reciprocal will be 1/x.

Given, their sum is -25/12

→x+1/x=-25/12

(x²+1)/x=-25/12

12x²+12+25x=0

12x²+16x+9x+12=0

4x(3x+4)+3(3x+4)=0

(4x+3)(3x+4)=0

Therefore, the number is -3/4 or -4/3

I hope this will help u ;)

Answer 2

Hi ,

Let us assume the number = x

it's reciprocal = 1/x

according to the problem given,

x + 1/x = - 25/12

( x² + 1 )/x = -25/12

12( x² + 1 ) = -25x

12x² + 25x + 12 = 0

12x² + 16x + 9x + 12 = 0

4x( 3x + 4 ) + 3( 3x + 4 ) = 0

( 3x + 4 ) ( 4x + 3 ) = 0

Therefore ,

3x + 4 = 0 or 4x + 3 = 0

3x = -4 or 4x = -3

x = -4/3 or x = -3/4

Required number = x = -4/3 or -3/4

I hope this helps you.

: )