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q = √2 - 3
a) 2p + q = 2(√2 + 3) + (√2 - 3)
= 32 + 3
b) pq = (√2 + 3)(√2 - 3)
= 2 - 3
= - 1
c) p² + q² = (√2 + 3)² + (√2 - 3)²
= 11 + 2√6 + 11 - 2√6
= 22
d) p/q = (√2 + 3)/(√2 - 3) * (√2 + 3)/(√2 + 3)
= (11 + 2√6)/(- 7)
= (-1/7)(11 + 2√6)