Question 283295
1. Two consecutive integers are best shown as:  x and x+1.
(x)(x+1) = 600
x^2 + x -600 = 0
(x+25)(x-24) = 0
x=-25 or x=24
Answer:
The two consecutive integers are either 24 & 25 or -25 & -24.
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2. Two consecutive even integers are best shown as:  x and x+2.
(x)(x+2) = 1848
x^2+2x-1848 = 0
(x+44)(x-42) = 0
x = -44 or x=42
Answer:
The consecutive even integers are either -44 and -42 or 42 and 44.
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3. Two positive integers differ by 12 is best shown as:  x and x+12
(x)(x+12)=405
x^2 + 12x -405 = 0
(x+27)(x-15) = 0
x=-27 or x=15
BUT we are told positive numbers only,
x = 15 and x+12 = 27
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Done