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Question 819454: Find three consecutive even integers such that the square of the sum of the first and second integers is equal to twice the third integer.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! (i + j)(i + j) = 2k
k = i + 4
j = i + 2
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(i + j)(i + j) = 2k
ii + 2ij + jj = 2k
ii + 2i(i + 2) + (i + 2)(i + 2) = 2(i + 4)
ii + 2ii + 4i + ii + 4i + 4 = 2i + 8
4ii + 6i - 4 = 0
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the above quadratic equation is in standard form, with a=4, b=6, and c=-4
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to solve the quadratic equation, by using the quadratic formula, plug this:
4 6 -4
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
i = 0.5
i = -2
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the problem definition rules out 0.5 as a root, but does not rule out negative integers
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answer:
i = -2
j = 0
k = 2
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