Question:
The product of two consecutive positive integers is 306. Find the integers.
Solution:
Let the two consecutive positive integers be x and (x + 1).
According to the given condition,
$x(x+1)=306$
$\Rightarrow x^{2}+x-306=0$
$\Rightarrow x^{2}+18 x-17 x-306=0$
$\Rightarrow x(x+18)-17(x+18)=0$
$\Rightarrow(x+18)(x-17)=0$
$\Rightarrow x+18=0$ or $x-17=0$
$\Rightarrow x=-18$ or $x=17$
∴ x = 17 (x is a positive integer)
When x = 17,
x + 1 = 17 + 1 = 18
Hence, the required integers are 17 and 18.
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