That means that you calculate the cubes of two numbers, and then either add or subtract them.
1
Sum and difference of two cubes is factored this way : a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2)
There's a formula for the sum of cubes. (3x + 4)(9x^2 - 12x + 16)
The sum of the cubes of the first 100 whole numbers is 25,502,500.
The formula for the sum of a series of cubes is as follows: 13 + 23 + 33 + ... + n3 = [n2*(n+1)2]/4 You may notice that this is the same as the square of the sum 1 + 2 + 3 + ... + n.
a3 + b3
That means that you calculate the cubes of two numbers, and then either add or subtract them.
1
The sum of their squares is 10.
1
50%
Sum and difference of two cubes is factored this way : a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2)
You get the sum of 11 two ways; 5,6 and 6,5.
23 = 8, 33 = 27. Sum 35, difference 19...
a3+ b3 = (a + b)(a2 - ab + b2)
According to Ramanujan, it's the lowest number that can be expressed in two different ways as the sum of two cubes (the cubes of 12 and 1; the cubes of 10 and 9). It 's the answer.