Question 230197
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I have to presume that you mean "3 consecutive <i>integers</i>" because "3 consecutive numbers" doesn't make any sense unless the numbers are at least restricted to the integers.


Let *[tex \Large x] represent the smallest integer.  Then the next consecutive integer is *[tex \Large x + 1], and the next one after that is *[tex \Large (x + 1) + 1\ =\ x + 2].


The product of the smallest two is then:  *[tex \Large x(x+1)\ =\ x^2 + x]


28 less than the square of the largest is:  *[tex \Large (x+2)^2-28\ =\ x^2+4x+4-28\ =\ x^2+4x-24]


These two quantities are equal so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 4x\ -\ 24\ =\ x^2\ +\ x]


Solve for *[tex \Large x] to find the smallest number, then count to get the other two.



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