Express the following numbers as the sum of two consecutive positive integers.
(a) 19
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i) Let us consider the consecutive positive integers be x,x+1.
According to the problem,
x+(x+1)=15
2
or, 2x+1=225
or, 2x=224
or, x=112.
The required integers are 112,113.
ii) Let us consider the consecutive positive integers be x,x+1.
According to the problem,
x+(x+1)=21
2
or, 2x+1=441
or, 2x=440
or, x=220.
The required integers are 220,221.
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