If x is a whole number > 2, then x2(x2-1) is always divisible by?
options:
1) 12
2) 24
3) 12-x
4) any multiple of 12 lesser than the expression
Answers
Solution :-
Given that
x > 2 , x is a whole number
The possible values of x = 3,4,5,6,...
If x = 3 then the value of x²(x²-1)
= 3²(3²-1)
= 9 (9-1)
= 9×8
= 72
= 6×12
= Multiple of 12
It is divisible by 12
If x = 4 then the value of x²(x²-1)
= 4²(4²-1)
= 16(16-1)
= 16(15)
= 240
= 20×12
= multiple of 12
It is divisible by 12
If x = 5 then the value of x²(x²-1)
= 5²(5²-1)
= 25(25-1)
= 25(24)
= 600
= 50×12
= multiple of 12
It is divisible by 12
If we continue this process then we get the values 72, 240,600.... which are multiples of 12 .
They are always divisible by 12
Answer :-
If x>2 , x is a whole number then x²(x²-1) is always divisible by 12.
Step-by-step explanation:
Solution :-
Given that
x > 2 , x is a whole number
The possible values of x = 3,4,5,6,...
If x = 3 then the value of x²(x²-1)
= 3²(3²-1)
= 9 (9-1)
= 9×8
= 72
= 6×12
= Multiple of 12
It is divisible by 12
If x = 4 then the value of x²(x²-1)
= 4²(4²-1)
= 16(16-1)
= 16(15)
= 240
= 20×12
= multiple of 12
It is divisible by 12
If x = 5 then the value of x²(x²-1)
= 5²(5²-1)
= 25(25-1)
= 25(24)
= 600
= 50×12
= multiple of 12
It is divisible by 12
If we continue this process then we get the values 72, 240,600.... which are multiples of 12 .
They are always divisible by 12
Answer :-
If x>2 , x is a whole number then x²(x²-1) is always divisible by 12.