If  a + b = 5  and  ab = 6 , then find the value of 

4(a² - b²) – a³ + b³,    if a > b .

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Solve the system of equations:

ìa + b = 5 
í
î   ab = 6

Solve the first for b:

              a + b = 5
                  b = 5 - a

Substitute 5 - a for b in the second equation of the system:

                 ab = 6
           a(5 - a) = 6
            5a - a² = 6
       -a² + 5a - 6 = 0 
        a² - 5a + 6 = 0
     (a - 3)(a - 2) = 0

     a - 3 = 0;   a - 2 = 0
         a = 3;       a = 2

     b = 5 - a    b = 5 - a 
     b = 5 - 3    b = 5 - 2
     b = 2        b = 3

There are two solutions (a,b) = (3,2) and (a,b) = (2,3)

But we are told that a > b so we choose the first and
discard the second, so a=3 and b=2 

Therefore the value of

4(a² - b²) – a³ + b³   is

4(3² - 2²) – 3³ + 2³

 4(9 - 4) - 27 + 8 

     4(5) - 19 

       20 - 19

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Edwin