Question 198707
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1st integer:  *[tex \Large x]


Next consecutive even integer: *[tex \Large x + 2]


Sum of the squares:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2 + (x + 2)^2 = 340]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x^2 + 4x + 4 = 340]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x^2 + 4x - 336 = 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2 + 2x - 168 = 0]


Solve the quadratic for *[tex \Large x] to get the first integer.  Hint: It factors.  Since the constant is a large negative and the first degree term is quite small, the factors must be of opposite signs and have a difference of 2.  Investigate the square root of 168 to get an idea of where to start.  You will get two roots, but exclude the negative one because the problem asks for positive integers.


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