If α,β and γ are the roots of the equation x3-7x+7=0, then 1α4+1β4+1γ4=
73
37
47
74
Explanation for the correct option:
Step 1. Find the value of 1α4+1β4+1γ4:
⇒∑α=0,∑αβ=–7 and αβɣ=–7
⇒∑αβ=αβɣ
Also, ∑1α=1
Step 2. By squaring both sides, we get
∑1α2=1
⇒∑1α2+2∑ααβγ=1
⇒ ∑1α2=1 ∵∑α=0
Step 3. By squaring again both sides, we get
∑1α22=1
⇒∑1α4+2∑α2αβγ2=1
∑1α4=1-2∑α2αβγ2
=1-214-72=1-2849=1-47=37
Hence, Option ‘B’ is Correct.