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

Options

A. 2
B. 4
C. 8
D. 12

Answer

C

Explanation

Let `{(a,b):2a^(2)+3b^(2)=35,a,binZ}`
Now, `2a^(2)+3b^(2)=35`
`implies" "2a^(2)=35-3b^(2)`
`implies" "a^(2)=((35-3b^(2))/(2))`
Since, a, b `in` Z. Hence, it is only possible when `b = +-3` or `b=+-1`.
We have, `a^(2)=(35-27)/(2)=(8)/(2)=4`
`implies" "a^(2)=4`
`implies" "a=+-2`
or `" "a^(2)=(35-3)/(2)=(32)/(2)=16`
`implies" "a^(2)=16`
`implies" "a=+-4`
Hence, solution sets are `{+-4,+-1}" or "{+-2,+-3}`.