SOLUTION: Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.
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Question 148763: Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.
You can put this solution on YOUR website! Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.
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Let x = 1st consecutive even integer
x+2 = 2nd consecutive even integer
x+4 = 3rd consecutive even integer
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(x+4)^2 - 76 = (x+2)^2
expanding the polynomial:
x^2+8x+16 - 76 = x^2+4x+4
subtracting x^2 from both sides:
8x+16 - 76 = 4x+4
8x - 60 = 4x+4
8x = 4x+64
4x = 64
x = 16
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Therefore the three even integers are:
16, 18, and 20
