James and billy have ages that are two consecutive odd integers whose products is 399. Use a quadratic equation to find out the age of each boy if james is the younger of the two boys?

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I dont understand how to make the equation and please provide the answers

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Answer 1 · 2018-08-04T12:45:30

Ages of James and billy are #19 and 21# years respectively.

Let the two consecutive odd integers be #(2 n-1) and (2 n+1)#

Their product is #(2 n-1)(2 n+1)=399# or

# (2 n)^2- 1^2= 399 or 4 n^2= 399+1 or 4 n^2=400#

#:. n^2= 400/4 or n^2= 100 :. n = +- 10 :. n = 10#

Since age cannot be negative # n!=-10#.

When #n=10 , 2 n-1= 19 and 2 n +1= 21# Therefore,

ages of James and billy are #19 and 21# years respectively. [Ans]