If k is the largest possible real number such that p4 +

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If k is the largest possible real number such that p⁴ + q⁴ = (p² + kpq + q²)(p² – kpq + q²), then the value of k is

p⁴ + q⁴ = (p²)² + (q²)²
= (p² + q²)² – 2p²q²
= (p² + q²)² – (√2pq)²
= (p² + q² + √2pq)(p² + q² – √2pq)