Let the set C = ( x , y ) ∣ x 2 - 2 y = 2023 , x , y ∈ ℕ . Then ∑ ( x , y ) ∈ C ( x + y ) is equal to _______.

Question

Let the set C = ( x , y ) ∣ x 2 - 2 y = 2023 , x , y ∈ ℕ . Then ∑ ( x , y ) ∈ C ( x + y ) is equal to _______.,

MARKS App · Accepted Answer

Given x 2 - 2 y = 2023 ⇒ x 2 = 2 y + 2023 Now, if y = 1 we get, ⇒ x 2 = 2025 ⇒ x = 45 And there is no other value which will satisfy the above equation, Hence, x = 45 & y = 1 So, ∑ ( x , y ) ∈ C ( x + y ) = 45 + 1 = 46

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