Question

if 2009=p^a×q^b, where p and q are prime numbers, then find the value of p+q.

Answer 1

Given : 2009 = $p^{a} q^{b}$
Where p and q are prime numbers
We know that 2009 = 7 × 7 × 41 = $7^{2} * 41^{1}$
Comparing both equations, we get:-
p = 7 
q = 41 
a = 2 and b = 1
Therefore,
p + q = 7 + 41 = 48
48 is the answer.

Answer 2

2009 = p^a * q^b. 
2009 = 41 * 49 = 41 * 7^2. 
2009 = 41 * 7^2 = 41^1 * 7^2: 
p = 41 and q = 7. 
Therefore, p + q = 41 + 7 = 48.