Question

prove that if A and B are both different odd positive integers, then A³-B³ is even but not always divisible by 4

Answer 1

♧♧HERE IS YOUR ANSWER♧♧

Let us consider the odd positive integers are

A = (2n + 3) and B = (2n + 1).

Now,

A³ - B³

= (2n + 3)³ - (2n + 1)³

= (8n³ + 36n² + 54n + 27) - (8n³ + 12n² + 6n + 1)

= 24n² + 48n + 26

= 2 × (12n² + 24n + 13), which is an even number for ∀n belongs to |N.

But is is not always divisible by 4.

When n = 1, A³ - B³ = 98, not divisible by 4.

When n = 2, A³ - B³ = 218, not divisible by 4
. . .
. . .
. . .

Hence, proved.

♧♧HOPE THIS HELPS YOU♧♧

Answer 2

hope this help you........