The sum of a number and its reciprocal is -25/12. Find the numbers.?

Answer 1

x + 1 / x = - 25/12
12 x ² + 12 = - 25 x
12x ² + 25 x + 12 = 0
x = [ - 25 ± √(625 - 576) ] / 24
x = [- 25 ± √49 ] / 24
x = [ - 25 ± 7 ] / 24
x = - 18 / 24 , x = - 32 / 24
x = - 3 / 4 , x = - 4 / 3

Answer 2

a + 1/a = -25/12

a^2 + 1 + (25/12) a = 0

12a^2 + 12 + 25a = 0

12a^2 + 25a + 12 = 0

12a^2 + 16a + 9a + 12 = 0

4a(3a + 4) + 3(3a + 4) = 0

(3a+4)(4a+3) = 0

a = -4/3 or - 3/4