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Math - marie flore joseph, Monday, April 5, 2010 at 10:37pm
the difference of the squares of two consecutive odd integers is 24 find the integers
Let the first integer be x, then the next consecutive off integer is x+2
(x+2)^2 - x^2 = 24
x^2 + 4x + 4 - x^2 = 24
4x = 20
x = 5
the two integers are 5 and 7
check to see if they meet the condition you stated.
To solve the given problem, we need to find two consecutive odd integers whose squares have a difference of 24.
Let's assume the first odd integer as x. Since the two integers are consecutive, the next odd integer will be x + 2.
The square of the first odd integer is x^2.
The square of the second odd integer is (x + 2)^2.
According to the problem, the difference of these two squares is 24. So we can set up the following equation:
(x + 2)^2 - x^2 = 24
Expanding and simplifying the equation:
(x^2 + 4x + 4) - x^2 = 24
4x + 4 = 24
Now, isolate the variable by subtracting 4 from both sides of the equation:
4x = 20
Finally, divide both sides of the equation by 4 to solve for x:
x = 5
Therefore, the first odd integer is 5, and the next consecutive odd integer is 7 (since x + 2 = 5 + 2 = 7).
To verify if these integers meet the condition, we can substitute the values back into the original equation:
(7)^2 - (5)^2 = 49 - 25 = 24
Therefore, the answer is correct, and the two consecutive odd integers that satisfy the given condition are 5 and 7.
To check if the integers 5 and 7 meet the condition, we can calculate the difference of their squares.
The square of 5 is 5^2 = 25.
The square of 7 is 7^2 = 49.
The difference of their squares is 49 - 25 = 24, which matches the condition given in the question.
Thus, the integers 5 and 7 satisfy the condition.