Solve for a+b given a^2=16 and ab=16

Published on April 3, 2026

Algebra

Solve for the value of a+b using the given equations a^2=16 and ab=16. Determine possible values for 'a' and then find corresponding 'b' values to calculate a+b.

Question

Answer

The problem presents a system of equations:

First, we need to solve for the possible values of

from the first equation,

.
Taking the square root of both sides, we get

, which means

Now, we consider each possible value of

and use the second equation,

, to find the corresponding value of

Case 1: If

.
Substitute

into the second equation:

Divide both sides by 4:

In this case,

and

.
Now, we calculate

for this case:

Case 2: If

.
Substitute

into the second equation:

Divide both sides by -4:

In this case,

and

.
Now, we calculate

for this case:

So, there are two possible values for

, which are 8 and -8. The problem does not specify that

and

must be positive. If there is an implicit assumption that the variables are positive real numbers, then only Case 1 would be considered, and the answer would be 8. However, without such an explicit constraint, both solutions are valid. Typically, in such problems presented without additional context, all real number solutions are considered.

The question asks for “a + b = ?”. Since there are two possible scenarios, there are two possible answers.

Final Answer: The final answer is