if ab+a+b=76 find a+b​

We can rewrite the equation by adding 1 to both sides:

\( ab + a + b + 1 = 77 \)

Factor the left side: \( (a+1)(b+1) = 77 \).

Since \( a \) and \( b \) are positive integers, \( a+1 \) and \( b+1 \) are positive integer factors of 77. The factor pairs of 77 are (1, 77) and (7, 11).

If \( a+1 = 1 \) and \( b+1 = 77 \), then \( a = 0 \), \( b = 76 \), giving \( a+b = 76 \).

If \( a+1 = 7 \) and \( b+1 = 11 \), then \( a = 6 \), \( b = 10 \), giving \( a+b = 16 \).

Usually, in such problems, \( a \) and \( b \) are considered natural numbers (positive integers), so the typical answer is \( a+b = 16 \).

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