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If the sum of three consecutive integers is equal to their product ,then find the integers?
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If the sum of three consecutive integers is equal to their product ,th...
Problem: If the sum of three consecutive integers is equal to their product, then find the integers.
Solution:
Let the three consecutive integers be x, x+1, and x+2.
According to the problem, we have:
x + (x+1) + (x+2) = x(x+1)(x+2)
Simplifying the left side:
3x + 3 = x^3 + 3x^2 + 2x
Simplifying the right side:
x^3 + 3x^2 + 2x = x^2(x+2) + x(x+2) = x(x+1)(x+2)
Therefore, we have:
3x + 3 = x(x+1)(x+2)
Expanding the right side:
3x + 3 = x^3 + 3x^2 + 2x
Subtracting 3x + 3 from both sides:
0 = x^3 + 3x^2 + 2x - 3x - 3
Simplifying:
0 = x^3 + 3x^2 - x - 3
We can solve this equation by trying different values of x. We find that x=1 is a solution.
Therefore, the three consecutive integers are:
1, 2, and 3
Answer: The three consecutive integers are 1, 2, and 3.
Solution:
Let the three consecutive integers be x, x+1, and x+2.
According to the problem, we have:
x + (x+1) + (x+2) = x(x+1)(x+2)
Simplifying the left side:
3x + 3 = x^3 + 3x^2 + 2x
Simplifying the right side:
x^3 + 3x^2 + 2x = x^2(x+2) + x(x+2) = x(x+1)(x+2)
Therefore, we have:
3x + 3 = x(x+1)(x+2)
Expanding the right side:
3x + 3 = x^3 + 3x^2 + 2x
Subtracting 3x + 3 from both sides:
0 = x^3 + 3x^2 + 2x - 3x - 3
Simplifying:
0 = x^3 + 3x^2 - x - 3
We can solve this equation by trying different values of x. We find that x=1 is a solution.
Therefore, the three consecutive integers are:
1, 2, and 3
Answer: The three consecutive integers are 1, 2, and 3.
Community Answer
If the sum of three consecutive integers is equal to their product ,th...
It's 1,2&3.
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If the sum of three consecutive integers is equal to their product ,then find the integers?
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If the sum of three consecutive integers is equal to their product ,then find the integers? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the sum of three consecutive integers is equal to their product ,then find the integers? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of three consecutive integers is equal to their product ,then find the integers?.
If the sum of three consecutive integers is equal to their product ,then find the integers? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the sum of three consecutive integers is equal to their product ,then find the integers? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of three consecutive integers is equal to their product ,then find the integers?.
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