Question

if α,β,γ are such that α+β+γ=2,
α^2+β^2+​γ^2=6 and α^3+β^3+γ^3=8 then find the value of α^4+β^4+γ^4 is​

Answer 1

Answer:

(α+β+γ)  

2  =α  

2  +β  

2  +γ  

2  +2(αβ+βγ+γα)⇒αβ+βγ+γα=−1

And α  

3  +β  

3  +γ  

3  −3αβγ=(α+β+γ)(α  

2  +β  

2 +γ  

2  −αβ−βγ−γα)⇒αβγ=−2

Then (α  2  +β 2  +γ  2  )  

2  =∑α  

4  +2∑β  

2 γ  2  =∑α  

4  +2((∑βγ)  

2  −2αβγ(α+β+γ))   +β  4  +γ  

4  =36−2((−1)  

= 18