If α,β and γ are the roots of equation x3-3x2+x+5=0 then y=∑ α2+αβγ satisfies the equation
y3+y+2=0
y3-y2-y-2=0
y3+3y2-y-3=0
y3+4y2+5y+20=0
Given equation x3-3x2+x+5=0
Then α+β+γ=3, αβ+βγ+γα=1, αβγ=-5
y=∑ α2+αβγ=(α+β+γ)2-2(αβ+βγ+γα)+αβγ
=9-2-5=2
∴y=2