We have a + b = 9 and a – b= 2. The easiest way to find a^4 + b^4 would be to first use the given values of a + b and a – b to determine a and b.

a + b = 9 … (1)

a – b = 2 … (2)

(2) + (1)

=> a + b + a – b = 9 + 2

=> 2a = 11

=> a = 11/2

substituting this in (1)

=> 11/2 + b = 9

=> b = 9 – 11/2

=> b = (18 – 11) /2

=> b = 7/2

a^4 + b^4

=> (11/2)^4 + (7/2)^4

=> 14641 / 16 + 2401 / 16

=> 17042 / 16

=> 8521 / 8

**Therefore a^4 + b^4 = 8521/8**

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