The number of elements in the set (a, b): 2a2 + 3b2 = 35, a, b ∈ Z, where Z is the set of all integers, is

Question

The number of elements in the set (a, b): 2a2 + 3b2 = 35, a, b ∈ Z, where Z is the set of all integers, is (A) 2 (B) 4 (C) 8 (D) 12

Tardigrade Admin · Accepted Answer

Given set is (a,b): 2a2 + 3b2 = 35, a,b∈ Z We can see that, 2(±2)2 + 3(±3)2 = 35 and 2(±4)2 + 3(±1)2 = 35 ∴ (2, 3), (2, - 3), (-2, - 3), (-2, 3), (4, 1), (4, - 1), (- 4, -1), (-4, 1) are 8 elements of the set . ∴ n = 8.

Q. 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

2

4

8

12

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 $2 (\pm 4)^{2} + 3 (\pm 1)^{2} = 35$
$∴ (2, 3), (2, - 3), (- 2, - 3), (- 2, 3), (4, 1), (4, - 1),$
$(- 4, - 1), (- 4, 1)$ are 8 elements of the set . $∴ n = 8$ .

Q. The number of elements in the set {(a,b):2a2+3b2=35,a,b∈Z}, where Z is the set of all integers, is

2

4

8

12

Given set is {(a,b):2a2+3b2=35,a,b∈Z} We can see that, 2(±2)2+3(±3)2=35 and 2(±4)2+3(±1)2=35 ∴(2,3),(2,−3),(−2,−3),(−2,3),(4,1),(4,−1), (−4,−1),(−4,1) are 8 elements of the set . ∴n=8.

Q. 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

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 $2 (\pm 4)^{2} + 3 (\pm 1)^{2} = 35$
$∴ (2, 3), (2, - 3), (- 2, - 3), (- 2, 3), (4, 1), (4, - 1),$
$(- 4, - 1), (- 4, 1)$ are 8 elements of the set . $∴ n = 8$ .