x is a positive integer ,is x divisible by 2?
1)x^3+x is divisible by 4
2)5x+4is divisible by 6
KINDLY SHARE THE METHOD OF SOLVING
1: (x^3+x) = 4k
x (x^2+1) = 4k, where k is an integer
either x or x^2+1 is divisible by 4. if x^2+1 were to divided by 4, x^2 must be odd. in that case, x is also odd. but square of any odd plus 1 cannot be a multiple of 4. for ex:
3^2+1 = 10, which is not divisible by 4.
5^2+1 = 26, which is not divisible by 4.
7^2+1 = 50, which is not divisible by 4.
9^2+1 = 81, which is not divisible by 4.
so x must be an even and also a multiple of 4. so suff...
2: 5x + 4 = 6m, where m is an integer
if 6 were to divide 5x+4 evenly, 5x+4 must be an even integer. in that case, 5x also be an even integer and eventually x is to an even integer.