How can one solve this without expanding. \(\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}\right\rbrace}\

Samara Richard

Samara Richard

Answered question

2022-03-24

How can one solve this without expanding.
 If a+b+c=1,ab+bc+ca=2

 and abc=3. What is the value  

 of a4+b4+c4 ? 

Answer & Explanation

diocedss33

diocedss33

Beginner2022-03-25Added 12 answers

a, b, c are the roots of x3x2+2x3=0
a2+b2+c2=(a+b+c)22(ab+bc+ac)=12(2)=3
Since x3=x22x+3
a3+b3+c3=(a2+b2+c2)2(a+b+c)+9=32(1)+9=4
Since x4=x32x2+3x
a4+b4+c4=42(3)+3(1)=13

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