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Step-by-step explanation:
1. a² + 1/a² :
a² = (3+√5)²/(2)² = 9+6√5 / 4 —(From formula)
1/a² = 4 / 9+6√5
So , a² + 1/a² = 9+6√5 (8)/ 9+6√5(4) = 2 — (LCM)
So , a² + 1/a² = 2
2. a³ + 1/a³ :
a³ = (3+√5)³ / (2)³ = (27 +27√5 + 45 + 5√5) / 8 = (9+ 4√5) —(Formula)
1/a³ = 1/9+4√5
So, a³ + 1/a³ = 2(9+4√5)/9+4√5 = 2—(LCM)
So , a³ + 1/a³ = 2
Hope it helps you
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