Question

if a=3+2√2 then the value of a∧6+a∧4+a∧2+1/a∧3

Answer 1

a⁶ + a⁴ + 1/a³

a = 3 + 2√2

1/a = 1/(3+ 2√2)  = 3- 2√2

(a⁶ + a⁴ + 1)/a³ =   a⁶ + a⁴ + 1    = a³ + a + 1/a + 1/a³

                                  a³

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

27 + 16√2 + 54√2 + 72 + 3 + √2 + 3 √2 + 27 - 16√2 - 54√2 + 72

= 204