The number of ordered pairs x , y of positive integers satisfying 2 x + 3 y = 5 x y is

Step-by-step solution

2 x + 3 y = 5 x y Clearly x = y = 1 satisfy the relation Take x > y 3 x > 3 y 2 x + 3 x > 2 x + 3 y 2 x + 3 x > 5 x y this is false 5 x y > 5 x = 2 + 3 x > 2 x + 3 x Similarly there is no solution for x < y Hence x = y Hence only x = y = 1 satisfy the given equation ( 2 x + 3 x = 5 x y is not true for x ∈ N - 1 )