Sets Relations And Functions Question 5
Question: The number of elements in the set $\{(a, b): 2 a^2+3b^2=35, a, b \in \mathrm{Z}\}$, where Z is the set of all integers is
Options:
A) 2
B) 4
C) 8
D) 12
Show Answer
Answer:
Correct Answer: C
Solution:
- [c]Given set is $ \{(a,b):2a^{2}+3b^{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. $
BETA
