If a and b are nonzero integers such that ab prove that 2a26

If a and b are nonzero integers such that a|b, prove that 2a^2|6b^2. Use a direct proof and the defintion of divisibility.

Solution

a and b are non zero integers ,a/b

Which implies that b=ak for some k in Z.

b^2=a^2k\'

6b^2=6a^2k\'=2a^2(3k\')

6b^2=2a^2(3k\')=2a^2l,l=3k\'

which implies thst 2a^2/6b^2