x² + y²
= ( √2 + 1 )² + ( √2 - 1 )²
= 2 + 2 √2 + 1 + 2 - 2 √2 + 1
= 6
Réponse:
Step-by-step solution:
1. Calculate x²:
x = √2 + 1
x² = (√2 + 1)²
x² = 2 + 2√2 + 1
x² = 3 + 2√2
2. Calculate y²:
y = √2 - 1
y² = (√2 - 1)²
y² = 2 - 2√2 + 1
y² = 3 - 2√2
3. Now, substitute the values of x² and y² into the expression x² + y²:
x² + y² = (3 + 2√2) + (3 - 2√2)
x² + y² = 3 + 2√2 + 3 - 2√2
x² + y² = 6
Final answer: 6
