0
1 ------ a+b=4
2 ------ ab=2 ====> 3. b = 2/a
Sub 3 into 1 ===> a + 2/a = 4
mutiply both sides by a ===> a2 +2 -4a = 0
use quadratic formula to find a ==> a= 2 +sqrt(2) or a' = 2- sqrt(2)
use these two values of a to find a value for b using equation 3 ===> using a, b= 2-sqrt(2) and using a', b= 2+sqrt(2)
hence a4 + b4 = (2+sqrt(2))4 + (2-sqrt(2))4 = 136 (for both values of a and b)
What else can I help you with?
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