Question

Answer Thisss oneee !!!!​

Answer 1

Answer:

198

Step-by-step explanation:

We can do this with minimal work.  In particular, we don't need to find a³.

Let's just work out a + 1/a.

1/a = 1 / ( 3 + 2√2 )

  = ( 3 - 2√2 ) / [ ( 3 + 2√2 ) ( 3 - 2√2 ) ]           [ multiplied numerator and denominator by the conjugate 3 - 2√2 ]

  = ( 3 - 2√2 ) / ( 3² - 2²√2² )

  = ( 3 - 2√2 ) / ( 9 - 8 )

  = 3 - 2√2

So

b = a + 1/a  = 3 + 2√2 + 3 - 2√2 = 6.

Next, expand b³ to get

b³ = ( a + 1/a )³ = a³ + 1/a³ + 3 ( a²/a + a/a² )

   = a³ + 1/a³ + 3 ( a + 1/a )

   = a³ + 1/a³ + 3b

=> a³ + 1/a³ = b³ - 3b = 6³ - 3×6 = 216 - 18 = 198