Solveeit Logo
Login

Question

Mathematics Question on Sets

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

A

2

B

4

C

8

D

12

Answer

8

Explanation

Solution

Given set is {(a,b):2a2+3b2=35,a,b∈Z(a,b) : 2a^2 + 3b^2 = 35, a,b\in Z} We can see that, 2(?2)2+3(?3)2=352(?2)^2 + 3(?3)^2 = 35 and 2(?4)2+3(?1)2=352(?4)^2 + 3(?1)^2 = 35 ∴(2,3),(2,−3),(−2,−3),(−2,3),(4,1),(4,−1),\therefore (2, 3), (2, - 3), (-2, - 3), (-2, 3), (4, 1), (4, - 1), (−4,−1),(−4,1)(- 4, -1), (-4, 1) are 8 elements of the set . ∴n=8\therefore n = 8.