Concept explainers
To find the four consecutive integers and choose the correct option.
Answer to Problem 24CR
Explanation of Solution
Given information:
There are four consecutive integers and the sum of the squares of second and third integers is 61.
Solution:
Let the second integer =
Let the third integer =
According to the question:
Sum of the squares of second and third integers is 61.
Therefore,
Expand the parenthesis using identity
Subtract 61 from both sides
Combine like terms
Divide each term by 2 to make above quadratic simpler to solve, we get
We need to compare above quadratic equation with standard quadratic equation
Now, we need to get the values of a, b and c and apply product sum rule to factor the quadratic.
On comparing quadratic
Product of value of a and c =
Value of
Now, we need to get two factors of -30 those add upto
We could see
So, split middle term
Now, making it into two groups and factor out Greatest Common Factor (GCF) of each group
Factor out
Factor out the common parenthesis
Applying zero product rule. Set each factor equal to 0 and solve for x .
If we take second integer -6, third integer would be
Therefore, the second integer is 5.
And third integer =
Fourth integer=
First integer =
Therefore, correct option is (a) {4, 5, 6, 7}.
Chapter 5 Solutions
Algebra: Structure And Method, Book 1
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