Question

plz solve guys.....necessary ​

Answer 1

Answer:

(i) α^4+β^4=7/25  (ii) α²/β+β²/α=2

Step-by-step explanation:

α,β are roots

5x²-5x+1=0

so α+β=-(-5)/5=1,αβ=1/5

α^4+β^4

=(α²+β²)²-2α²β²

=[(α+β)²-2αβ]²-2(αβ)²

=[1²-2*1/5]²-2*(1/5)²

=(1-2/5)²-2*1/25

=(3/5)²-2/25

=9/25-2/25

=7/25

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α²/β+β²/α

=(α³+β³)/αβ

=(α+β)(α²+β³-αβ)/αβ

=(α+β) [ (α+β)²-3αβ ]/αβ

=1*(1²-3*1/5)/(1/5)

=5*(1-3/5)

=5*2/5

=2

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