The number of elements in the set a , b : a 2 + b 2 = 50 ; a , b ∈ Z , where Z is the set of all integers, is

Step-by-step solution

a 2 + b 2 = 50 a = 1 ⇒ b 2 = 49 ⇒ b = ± 7 a = 2 , 3 , 4 , 6 do not give integer value of b . a = 5 ⇒ b 2 = 25 ⇒ b = ± 5 a = 7 ⇒ b 2 = 1 ⇒ b = ± 1 Similarly, a = - 1 ⇒ b = ± 7 a = - 5 ⇒ b = ± 5 a = - 7 → b = ± 1 ⇒ The required number of elements ( a , b ) = 12