Question

if a=3+2√2, then find the value of i) a²+1/a² ii)a³+1/a³​

Answer 1

a = 3 + 2√2

1/a = 1/(3 + 2√2)

= [1/(3 + 2√2)] x [3 - 2√2][3 - 2√2]

= (3 - 2√2)

(a6 + a4 + a2 +1) / a3

= (a3 + a + 1/a + 1/a3)

= (3 + 2√2)3 + (3 + 2√2) + (3 - 2√2) + (3 - 2√2)3

= (3 + 2√2)3 + (3 - 2√2)3 + (3 + 2√2) + (3 - 2√2)

=[2(3)3 + 6(3)(2√2)2] + [6]

= [54 + 144] + 6

= 198 + 6

= 204.

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