# Given a + b = 9 and a – b = 2, what is a^4 + b^4?

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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**

1st equation: a + b = 9

2nd equatrion: a - b = 2

since a+b=9, then a=9-b

replace this value of **a** to the 2nd equation.

since 2nd equation is a-b=2, then

(9-b)-b=2

9-b-b=2

9-2b=2

-2b=2-9

-2b=-7

b=7/2

given that b=7/2, substitute the value of **b** to one of the two equations

a+ (7/2) = 9

a=9-(7/2)

therefore a= 11/2

Given the a= 11/2 and b= 7/2,

a^4 + b^4

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

=(14641/16) + (2401/16)

=**(8521/8)**

a+b = 9 ...(1) .

a-b = 2....(2).

To find a^4+b^4.

(1)+(2): (a+b)+(a-b) = 2a = 9+2 = 11. So 2a/2 = 11/2 = 5.5. Or a = 5.5.

(1)-(2) : a+b -(a-b) = 2b = 9-2. So 2b = 7. Or b = 7/2 = 3.5.

Therefore a= 5.5 and b = 3.5.

=> a^4+b^4 = 5.5^4+3.5^4 = 1065.125.

**Therefore a^4+b^4 = 5.5^.4+3.5^4 = 1065.125**