Question

The sum of the reciprocal of two consecutive odd integers is 44/483.Write a rational equation to solve the problem.

Answer 1

Explanation:

Let consecutive odd integers be (2x + 1) and (2x + 3)

Their reciprocals are
`(1)/(2x + 1 )` and
`(1)/(2x + 3 )`

`(1)/(2x+1)+(1)/(2x+3)=(44)/(483)\\\\(1*(2x+3))/((2x+1)(2x+3))+(1*(2x+1))/((2x+3)(2x+1))=(44)/(483)\\\\(2x + 3 + 2x +1)/((2x + 1)(2x+3))=(44)/(483)\\\\(4x + 4)/(4x^(2)+8x+3)=(44)/(483)\\`

483*(4x+4) = 44*(4x² + 8x + 3)

483*4x + 483*4 = 44*4x² + 44*8x + 44*3

1932x + 1932 = 176x² + 352x + 132

176x² + 352x + 132 -1932x - 1932 = 0

Combine like terms

176x² + 352x - 1932x - 1932 + 132 = 0

176x² - 1580x - 1800 = 0

Divide the equation by 4

44x² - 395x - 450 = 0