If a and b are two odd positive integers, by which of the following integers is (a4 - b4) always divisible?
3
6
8
12
If a and b are odd numbers, then which of the following is even?
a + b + ab
a + b - 1
a + b + 1
a + b + 2ab
If a2 + b2 + c2 = 2 (a - b - c) - 3, then the value of 2a - 3b + 4c is
3
1
2
4
B.
1
a2 + b2 + c2 = 2 (a - b - c) - 3
⟹ (a2 - 2a + 1) + (b2 + 2b + 1) + (c2 + 2c + 1) = 0
⟹ (a - 1)2 + (b + 1)2 + (c + 1)2 = 0
∴ a - 1 = 0, b + 1 = 0, c + 1 = 0
⟹ a = 1, b = -1, c = -1
∴ 2a - 3b + 4c = 2(1) - 3(-1) + 4(-1) = 1