Question

find whether (root2, 3root2) is a solution of x-3y =9 or not

Answer 1

No
√2 - 3(3√2) = √2 - 9√2 = -8√2

which is not equal to 9

so it's not a root

any doubts, comment ;))

Answer 2

given x-3y=9
put x=√2 and y=3√2
now
√2-3(3√2)=√2-9√2=-7√2-----LHS
but RHS is 9
therefore it is not a solution