Algebra

[govind_raj_76]

If x is a number such that x^2 - 1 is divisible by 3, which of the following must be true.

a. x must be even.

b. x must be divisible by 3.

c. x must be odd.

d. x cannot be a multiple of 3.

e. x must leave a remainder of 1 when divided by 3.

Please explain how to solve this problem easily.

[aloneontheedge]

If x is a number such that x^2 - 1 is divisible by 3, which of the following must be true.

a. x must be even.

b. x must be divisible by 3.

c. x must be odd.

d. x cannot be a multiple of 3.

e. x must leave a remainder of 1 when divided by 3.

Please explain how to solve this problem easily.

Raj,
x^2 - 1 is divisible by 3 => (x-1)(x+1)/3
plug the values and check For instance x=2,3,4,5,6
which covers all scenarios.
This will show that X cannot be multiple of 3