Question 199101
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Let *[tex \Large x] represent the first integer.


The next consecutive even integer must then be *[tex \Large x + 2], and


The one after that must be *[tex \Large x + 4]


The product of the first two:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x(x + 2)]


Two less than five times the third:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5(x + 4) - 2]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x(x + 2) = 5(x + 4) - 2]


Distribute across the binomials, collect like terms, put the equation into standard form, and solve the quadratic.  You will get one negative odd integer root that you can discard, and one positive even root that is the value of the first integer.  The other two follow.


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