If the difference between two numbers is 6 and the difference between their squares is 60, what is the sum of their cubes ?
Answer & explanation
Correct answer: option 4
The difference between 2 numbers = 6
We know that,
a2 - b2 = (a - b)(a + b)
Let two number be a and b
According to the question,
a - b = 6 ----(1)
And,
a2 - b2 = 60
= 60 = (a + b)(a - b)
= 60 = 6(a + b)
= (a + b) = 10 ----(2)
From (1) and (2) get,
a = 8, b = 2
Sum of their cube = a3 + b3 = 83 + 23 = 512 + 8 = 520