Question

A+b+c=3, a^2+b^2+c^2=9, a^3+b^3+c^3=24 maka a^4.b^4+c^4 adalah

Answer 1

A^2+b^2+c^2=(a+b+c)^2-2(ab+bc+ca)
9=3^2-2(ab+bc+ca)
2(ab+bc+ca)=0
ab+bc+ca=0

a^3+b^3+c^3=(a+b+c)3-3(ab+bc+ca)(a+b+c)+3abc
24=3^3-3(0)(3)+3abc
24=27+3abc
3abc=-3
abc=-1

a^4+b^4+c^4=(a^2+b^2+c^2)^2-2(ab+bc+ca)^2+4(abc)(a+b+c)
a^4+b^4+c^4=9^2-2(0)^2+4(-1)(3)
a^4+b^4+c^4=81-0-12
a^4+b^4+c^4=69

Maaf kalau sulit dimengerti.