jika a+b =1 dan a^2+b^2=2,berapakah nilai a^4+b^4?
Matematika
ima306
Pertanyaan
jika a+b =1 dan a^2+b^2=2,berapakah nilai a^4+b^4?
1 Jawaban
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1. Jawaban arsetpopeye
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
ab = -1/2
a^2 + b^2 = 2
(a^2 + b^2)^2 = 2^2
a^4 + 2 a^2 b^2 + b^4 = 4
a^4 + b^4 + 2(ab)^2 = 4
a^4 + b^4 + 2(-1/2)^2 = 4
a^4 + b^4 + 2(1/4) = 4
a^4 + b^4 = 4 - 1/2 = 7/2 = 3 1/2 = 3,5