Number of elements in set { (a,,b):2{a^2} + 3{b^2} = 35,a,,b ∈ Z} , where Z is set of all integers

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1.Set Theory

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The number of elements in the set $\{ (a,\,b):2{a^2} + 3{b^2} = 35,\;a,\,b \in Z\} $, where $Z$ is the set of all integers, is

A

$2$

B

$4$

C

$8$

D

$12$

Solution

(c) Given set is $\{ (a,\,b):2{a^2} + 3{b^2} = 35,\;a,\,b \in Z\} $

We can see that, $2{( \pm 2)^2} + 3{( \pm 3)^2} = 35$ and $2{( \pm 4)^2} + 3{( \pm 1)^2} = 35$

$ \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$.

Standard 11

Mathematics

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