Question 226107
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Let *[tex \Large x] represent the smaller odd integer.  Then *[tex \Large x + 2] must represent the next consecutive odd integer.


The square of the larger one (*[tex \Large (x+2)^2]) is (=) 25 more than 8 times the smaller one (*[tex \Large 8x + 25])


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (x+2)^2 = 8x + 25]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2 + 4x + 4 -8x -25\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2 - 4x -21 = 0]


Solve the quadratic for *[tex \Large x] to get the value of the smaller integer.  It factors as one would presume since you are expecting integer answers.  You will get two roots.  Check to see if both of them are valid answers remembering that integers can be negative, but that the next consecutive integer to a negative integer has a smaller absolute value.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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