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Three numbers are in ratio2:3:4 the sum of their cubes is 33957 . Find the number?
Verified Answer
Three numbers are in ratio2:3:4 the sum of their cubes is 33957 . Find...
Let the numbers be 2x, 3x and 4x
sum of cubes = 33957
⇒(2x)^3 + (3x)^3 + (4x)^3 = 33957
⇒8x^3 + 27x^3 + 64x^3 = 33957
⇒99x^3 = 33957
⇒x^3 = 33957/99 = 343
⇒x = 3√343 = 7
Numbers are:
2x = 2�7 = 14
3x = 3�7 = 21
4x = 4�7 = 28
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Most Upvoted Answer
Three numbers are in ratio2:3:4 the sum of their cubes is 33957 . Find...
Given:
The numbers are in the ratio 2:3:4.
The sum of their cubes is 33957.
To find:
The numbers.
Solution:
Let's represent the three numbers in the ratio 2:3:4 as 2x, 3x, and 4x, where x is a common factor.
Step 1: Set up the equation:
The sum of their cubes is equal to 33957, so we can write the equation as:
(2x)^3 + (3x)^3 + (4x)^3 = 33957
Step 2: Simplify the equation:
Expanding the cubes, we get:
8x^3 + 27x^3 + 64x^3 = 33957
Simplifying further, we have:
99x^3 = 33957
Step 3: Solve for x:
Dividing both sides of the equation by 99, we get:
x^3 = 33957 / 99
Simplifying, we have:
x^3 = 343
Taking the cube root of both sides, we find:
x = ∛343
x = 7
Step 4: Find the numbers:
Now that we have the value of x, we can find the three numbers.
The numbers are:
2x = 2 * 7 = 14
3x = 3 * 7 = 21
4x = 4 * 7 = 28
Therefore, the three numbers are 14, 21, and 28.
Conclusion:
The numbers in the ratio 2:3:4, whose sum of cubes is 33957, are 14, 21, and 28.
The numbers are in the ratio 2:3:4.
The sum of their cubes is 33957.
To find:
The numbers.
Solution:
Let's represent the three numbers in the ratio 2:3:4 as 2x, 3x, and 4x, where x is a common factor.
Step 1: Set up the equation:
The sum of their cubes is equal to 33957, so we can write the equation as:
(2x)^3 + (3x)^3 + (4x)^3 = 33957
Step 2: Simplify the equation:
Expanding the cubes, we get:
8x^3 + 27x^3 + 64x^3 = 33957
Simplifying further, we have:
99x^3 = 33957
Step 3: Solve for x:
Dividing both sides of the equation by 99, we get:
x^3 = 33957 / 99
Simplifying, we have:
x^3 = 343
Taking the cube root of both sides, we find:
x = ∛343
x = 7
Step 4: Find the numbers:
Now that we have the value of x, we can find the three numbers.
The numbers are:
2x = 2 * 7 = 14
3x = 3 * 7 = 21
4x = 4 * 7 = 28
Therefore, the three numbers are 14, 21, and 28.
Conclusion:
The numbers in the ratio 2:3:4, whose sum of cubes is 33957, are 14, 21, and 28.
Community Answer
Three numbers are in ratio2:3:4 the sum of their cubes is 33957 . Find...
Three number are in the ratio 2 3 4 and sum of their cubes is 33957 find largest number
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Three numbers are in ratio2:3:4 the sum of their cubes is 33957 . Find the number?
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Three numbers are in ratio2:3:4 the sum of their cubes is 33957 . Find the number? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Three numbers are in ratio2:3:4 the sum of their cubes is 33957 . Find the number? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three numbers are in ratio2:3:4 the sum of their cubes is 33957 . Find the number?.
Three numbers are in ratio2:3:4 the sum of their cubes is 33957 . Find the number? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Three numbers are in ratio2:3:4 the sum of their cubes is 33957 . Find the number? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three numbers are in ratio2:3:4 the sum of their cubes is 33957 . Find the number?.
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