(a+sqrt(b))^(2) = 49+12 sqrt(b) where a and b are integers and b is prime and find a and b?

(a + √b)² = 49 + 12√b
a² + 2a√b + (√b)² = 49 + 12√b
a² + 2a√b + b = 49 + 12√b
(a² + b) + 2a√b = 49 + 12√b

Compare the rational parts and irrational parts on the both sides :
a² + b = 49 …… [1]
2a√b = 12√b …… [2]

From [2] :
2a = 12
a = 6

Substitute a = 6 into [1] :
6² + b = 49
36 + b = 49
b = 13

Hence a = 6, b = 13

a=6, b=13

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