SOLUTION: If a+b=1 and a^2 +b^2 = 2 find a^4 + b^4 = ??? Is it way too simple to say that the answer is 4?

Question 678585: If a+b=1 and a^2 +b^2 = 2
find a^4 + b^4 = ???
Is it way too simple to say that the answer is 4?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

a+b=1

(a+b)^2=1^2

a^2 + 2ab + b^2=1

(a^2 + b^2) + 2ab=1

(2) + 2ab=1

2ab=1-2

2ab=-1

(2ab)^2=(-1)^2

4a^2b^2=1

2a^2b^2=1/2

-------------------------

a^2 +b^2 = 2

(a^2 +b^2)^2 = 2^2

a^4 + 2a^2b^2+b^4 = 4

a^4 + 1/2 + b^4 = 4

a^4 + b^4 = 4 - 1/2

a^4 + b^4 = 7/2

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