The sum of the squares of two consecutive odd integers is 74. What are the two numbers?

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Answer 1 · 2016-08-04T16:49:35

Two integers are either #5# and #7# or #-7# and #-5#.

Let the two consecutive odd integers be #x# and #x+2#. As sum of their square is #74#, we have

#x^2+(x+2)^2=74# or

#x^2+x^2+4x+4=74# or

#2x^2+4x-70=0# or dividing by #2#

#x^2+2x-35=0# or

#x^2+7x-5x-35=0# or

#x(x+7)-5(x+7)=0# or

#(x+7)(x-5)=0#.

Hence #x=5# or #x=-7# and

Two integers are either #5# and #7# or #-7# and #-5#.