Three consecutive, odd, positive integers have the property that the product of the smaller two is 3 more than four times the sum of the larger two. Algebraically determine the three integers.
+23246 Let x, x + 2, and x + 4 represent the three consecutive positive integers.
The product of the smaller two: x(x + 2)
3 more than four times the sum of the larger two: 3 + 4[ (x + 2) + (x + 4) ]
x(x + 2) = 3 + 4[ (x + 2) + (x + 4) ]
x2 + 2x = 3 + 4[ 2x + 6 ]
x2 + 2x = 3 + 8x + 24
x2 + 2x = 27 + 8x
x2 - 6x - 27 = 0
(x - 9)(x + 3) = 0
x = 9
x + 2 = 11
x + 4 = 13
The numbers are x, x+2, and x+4
The equation is (x)(x+2) = 3 + (4)[(x+2)+(x+4)]
x2 + 2x = 3 + (4)(2x+6)
x2 + 2x = 3 + 8x + 24
rearrange x2 + 2x – 3 – 8x – 24 = 0
x2 – 6x – 27 = 0
factor (x – 9)(x + 3) = 0
x = 9 and x =–3 but discard –3 because the problem calls for positive numbers
The numbers are 9, 11, and 13
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