Diketahui a+b=1 dan a^2+b^2=2. Berapakah a^4+b^4?
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a + b = 1
(a + b)^2 = 1^2
a^2 + 2ab + b^2 = 1
2ab = 1 - (a^2 + b^2)
2ab = 1 - 2
ab = -1/2
a^2 + b^2 = 2
(a^2 + b^2)^2 = 2^2
a^4 + 2a^2b^2 + b^4 = 4
a^4 + 2(ab)^2 + b^4 = 4
a^4 + 2(-1/2)^2 + b^4 = 4
a^4 + 1/2 + b^4 = 4
a^4 + b^4 = 7/2 = 3 1/2 = 3,5