Concept explainers
To find: the two consecutive integers.
Answer to Problem 40CLR
The two consecutive integers are 4 and 5.
Explanation of Solution
Given information:
The sum of the squares of two consecutive integers is 9 greater than 8 times the smaller integer.
Calculation:
Let the first integer =
Let the second integer (consecutive) =
Sum of the squares of two consecutive integers =
8 times the smaller number =
Now,
Therefore,
Simplify Parenthesis:
Combine like terms
Subtract
Simplify
Factorize this quadratic equation using splitting middle term:
Now, factor it by grouping
Factor out
Factor out 2 from
We get
Factor out the common parenthesis:
Applying zero product rule. Set each factor equal to 0 and solve for x .
We don’t consider any negative value.
Therefore, the first integer is 4.
And second integer = x +1= 4+1=5.
Chapter 5 Solutions
Algebra: Structure And Method, Book 1
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