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Q.
The number of elements in the set {$(a, b) : 2a^2 + 3b^2 = 35, a, b \in Z$}, where Z is the set of all integers, is
Sets
Solution:
Given set is {$(a,b) : 2a^2 + 3b^2 = 35, a,b\in Z$}
We can see that, $2(±2)^2 + 3(±3)^2 = 35$
and $2(±4)^2 + 3(±1)^2 = 35$
$\therefore (2, 3), (2, - 3), (-2, - 3), (-2, 3), (4, 1), (4, - 1),$
$(- 4, -1), (-4, 1)$ are 8 elements of the set . $\therefore n = 8$.