If a2 + b2 = 2 and c2 + d2 = 1, then the value of

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If a² + b² = 2 and c² + d² = 1, then the value of (ad – bc)² + (ac + bd)² is

1. 4
  9
2. 1
  2
3. 1
4. 2

Correct Option: D

(ad – bc)² + (ac + bd)²
= a²d² + b²c² – 2abcd + a²c² +
b²d² + 2abcd
= a²d² + b²c² + a²c² +
b²d²
= a²d² + b²d² + b²c² + a²c²
= d²(a² + b²) + c²(b² + a²)
= (a² + b²) (c² + d²)
= 2 × 1 = 2