Answer:
Explanation:
To solve this problem, we can start by simplifying the expressions for a and b:
a = (√2+1)/(√2-1) * (√2+1)/(√2+1) = (3 + 2√2)
b = (√2-1)/(√2+1) * (√2-1)/(√2-1) = (1 - 2√2)
Now we can substitute these expressions into a²+ab+b² and simplify:
a² + ab + b²
= (3 + 2√2)² + (3 + 2√2)(1 - 2√2) + (1 - 2√2)²
= 9 + 12√2 + 8 + 3 - 4√2 - 4√2 - 2 + 4√2 + 4
= 24
Therefore, a²+ab+b² equals 24.