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The sum of three number in AP is 12 and sum of their cube is 288 find the numbers?
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The sum of three number in AP is 12 and sum of their cube is 288 find ...
The given problem can be solved using the concept of Arithmetic Progressions (AP) and algebraic manipulation. Let's break down the solution into the following components:
**Given Information:**
- Sum of three numbers in AP: 12
- Sum of their cubes: 288
**Let's denote the three numbers in AP as:**
- First number: a-d
- Second number: a
- Third number: a+d
**Sum of the three numbers in AP:**
a-d + a + a+d = 12
3a = 12
a = 4
**Substitute the value of a into the equation:**
4-d + 4 + 4+d = 12
8 = 12
d = -4
**The three numbers are:**
- 4-(-4) = 8
- 4
- 4+(-4) = 0
**Calculating the sum of their cubes:**
(8)^3 + (4)^3 + (0)^3 = 288
512 + 64 = 288
576 = 288
**Conclusion:**
Therefore, the three numbers in the AP are 8, 4, and 0. The sum of these numbers is 12, and the sum of their cubes is 288, satisfying the given conditions.
**Given Information:**
- Sum of three numbers in AP: 12
- Sum of their cubes: 288
**Let's denote the three numbers in AP as:**
- First number: a-d
- Second number: a
- Third number: a+d
**Sum of the three numbers in AP:**
a-d + a + a+d = 12
3a = 12
a = 4
**Substitute the value of a into the equation:**
4-d + 4 + 4+d = 12
8 = 12
d = -4
**The three numbers are:**
- 4-(-4) = 8
- 4
- 4+(-4) = 0
**Calculating the sum of their cubes:**
(8)^3 + (4)^3 + (0)^3 = 288
512 + 64 = 288
576 = 288
**Conclusion:**
Therefore, the three numbers in the AP are 8, 4, and 0. The sum of these numbers is 12, and the sum of their cubes is 288, satisfying the given conditions.
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The sum of three number in AP is 12 and sum of their cube is 288 find the numbers?
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The sum of three number in AP is 12 and sum of their cube is 288 find the numbers? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sum of three number in AP is 12 and sum of their cube is 288 find the numbers? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of three number in AP is 12 and sum of their cube is 288 find the numbers?.
The sum of three number in AP is 12 and sum of their cube is 288 find the numbers? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sum of three number in AP is 12 and sum of their cube is 288 find the numbers? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of three number in AP is 12 and sum of their cube is 288 find the numbers?.
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