Let the set C = { ( x , y ) ? x 2 - 2 y = 2023 , x , y ? N } . Then ? ( x , y ) ? C ( x + y ) is equal to ________ . JEE Main Mathematics Sets Relations And Functions

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Solution

Q.
Let the set $C = {(x, y) ∣ x^{2} - 2^{y} = 2023, x, y \in N}$ . Then $\sum_{(x, y) \in C} (x + y)$ is equal to ________ . [2024]

Ans.
(46)

$We have, x^{2} - 2^{y} = 2023 \Rightarrow 2^{y} = x^{2} - 2023$

$∴$ $Possible values of (x, y) are (45, 1)$

$S o, \sum_{(x, y) \in C} (x + y) = (45 + 1) = 46$

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