Question:
The difference between the squares of two consecutive numbers is 31. Find the numbers.
Solution:
Let the numbers be $x$ and $x+1$.
According to the question,
$(\mathrm{x}+1)^{2}-\mathrm{x}^{2}=31$
or $\mathrm{x}^{2}+2 \mathrm{x}+1-\mathrm{x}^{2}=31$
or $2 \mathrm{x}=31-1$
or $\mathrm{x}=\frac{30}{2}$
or $\mathrm{x}=15$
Thus, the numbers are 15 and 16 .
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