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The product of two consecutive integers is 106 less than twice the square of the next larger integer. Find the numbers.
Solution:
The first thing that we need to do is to analyze the given problem as follows:
Let x = be the first consecutive integer
x + 1 = be the second consecutive integer
x + 2 = be the third consecutive integer
If the word problem says "The product of two consecutive integers is 106 less than twice the square of the next larger integer.", then the working equation is
From the working equation, the value of x which is the first consecutive integer is
If you equate each factor to zero, then the values of x are -14 and 7.
Therefore, the three consecutive integers are -14, -13, and -12 or 7, 8, and 9.