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Let the two consecutive numbers be ( n ) and ( n + 1 ). The difference of their cubes can be expressed as ( (n + 1)^3 - n^3 ). Simplifying this gives ( 3n^2 + 3n + 1 ). Setting this equal to 169, we have the equation ( 3n^2 + 3n + 1 = 169 ). Solving for ( n ) yields ( n^2 + n - 56 = 0 ), which factors to ( (n - 7)(n + 8) = 0 ). Thus, ( n = 7 ) (ignoring ( n = -8 ) since we want positive consecutive numbers), giving the two consecutive numbers as 7 and 8.
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What are two consecutive numbers whose cubes add up to 1241?
8 and 9
What Consecutive numbers whose cubes differ by 631?
Let the two consecutive numbers be ( n ) and ( n+1 ). The difference of their cubes can be expressed as ( (n+1)^3 - n^3 = 3n^2 + 3n + 1 ). Setting this equal to 631 gives the equation ( 3n^2 + 3n + 1 = 631 ). Solving for ( n ) leads to ( 3n^2 + 3n - 630 = 0 ), which simplifies to ( n^2 + n - 210 = 0 ). Factoring or using the quadratic formula, we find ( n = 14 ) or ( n = -15 ). Therefore, the consecutive numbers are 14 and 15.
What is the consecutive numbers in mathematical algebra?
Consecutive numbers are whole numbers whose difference is 1.
Which are the Consecutive Numbers Whose Sum Is 22?
Any pair of consecutive numbers will have an odd total. 10 and 12 are consecutive even numbers that total 22.
The product of 3 consecutive odd numbers make 6873 what is it?
There is no set of 3 consecutive odd numbers whose product is 6,873. However, there is a set of 3 consecutive odd numbers whose sum is 6,873: 2289, 2291, and 2293.
What are two consecutive numbers whose cubes add up to 1241?
8 and 9
What are two consecutive numbers whose cubes produce a sum of 1241?
8 and 9
What 2 consecutive numbers whose squares differ by 17?
8
What are two consecutive numbers whose squares differ by 125?
62 and 63
What are two consecutive numbers whose squares differ by 31?
15 and 16
What is the consecutive numbers in mathematical algebra?
Consecutive numbers are whole numbers whose difference is 1.
What are two consecutive numbers whose sum is 126?
There are two consecutive even numbers. The numbers are 62 and 64.
Which are the Consecutive Numbers Whose Sum Is 22?
Any pair of consecutive numbers will have an odd total. 10 and 12 are consecutive even numbers that total 22.
What are the two consecutive whole numbers whose squares differ by 49?
24 and 25, which are (49-1)/2 and (49+1)/2
The product of 3 consecutive odd numbers make 6873 what is it?
There is no set of 3 consecutive odd numbers whose product is 6,873. However, there is a set of 3 consecutive odd numbers whose sum is 6,873: 2289, 2291, and 2293.
What is the two consecutive numbers whose product is 4160?
The numbers are 64 and 65.
What are two consecutive numbers whose sum is -15?
The numbers are -8, and -7.
