Algebra problem (9)

If:



then calculate:



Solution

Adding lines ...1 and ...2 gives:



We notice expression (a+b).
But how to eliminate the roots?
Say:



this changes the equations before into:



which reminds us of:
    (a+b)3 = a3 + 3a2b + 3ab2 + b3
So, multiply line ...5 by 3 and add line ...4 .
The result is:



Now substitute ..6 at line ...3 and insert factor 9/5 :



The answer is 73.