Question

What is the answer of this question? ​

Answer 1

9514 1404 393

Answer:

  970

Step-by-step explanation:

It turns out that the radical terms cancel, so the result is an integer. You can find the integer value using your calculator. It is ...

  (5 +2√6)³ +1/(5 +2√6)³ = 970

_____

The cube of 'a' is ...

  (5+2√6)³ = 5³ +3·5²·2√6 +3·5·(2√6)² +(2√6)³

  = 125 +3·50√6 +3·120 +48√6

  a³ = 485 +198√6

The reciprocal of this is ...

  b³ = 1/a³ = 1/(485 +198√6) = (485 -198√6)/(485² -6·198²) = (485 -198√6)/1

  b³ = 485 -198√6

Then the sum is ...

  a³ +b³ = (485 +198√6) +(485 -198√6) = 970