The product of two consecutive odd integers is 99, how do you find the integers?

Question

37298 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-16T17:14:25

Consecutive integers are #-11# and #-9# or #9# and #11#

Let the numbers be #(2x-1)# and #(2x+1)# as for any #x# these will be consecutive odd numbers. Hence

#(2x-1)(2x+1)=99# i.e.

#4x^2-1=99# or #4x^2-100=0# or #x^2-25=0#

i.e. #(x-5)(x+5)=0# i.e. #x=5 or -5#

Hence consecutive integers are #-11# and #-9# or #9# and #11#.