Answer: We want to find the value of (a+b)² given that a² + b² = 39 and ab = 4.
One way to approach this problem is to use the identity:
(a+b)² = a² + 2ab + b²
We can substitute the values we have into this identity:
(a+b)² = a² + 2ab + b²
= (a² + b²) + 2ab
= 39 + 2(4)
= 47
Therefore, (a+b)² = 47.
Explanation: