Search for: If α β and γ are the roots of the equation x3−7x+7=0, then 1α4+1β4+1γ4 is If α β and γ are the roots of the equation x3−7x+7=0, then 1α4+1β4+1γ4 is A7/3B3/7C4/7D7/4 Fill Out the Form for Expert Academic Guidance!l Grade ---Class 1Class 2Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12 Target Exam JEENEETCBSE +91 Preferred time slot for the call ---9 am10 am11 am12 pm1 pm2 pm3 pm4 pm5 pm6 pm7 pm8pm9 pm10pm Please indicate your interest Live ClassesBooksTest SeriesSelf Learning Language ---EnglishHindiMarathiTamilTeluguMalayalam Are you a Sri Chaitanya student? NoYes Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:Here, Σα=0,Σαβ=−7,αβγ=−7∴ 1α4+1β4+1γ4=α4β4+β4γ4+γ4α4α4β4γ4=Σα4β4α4β4γ4…………………………..(i)Now ,ΣαβΣαβΣαβΣαβ=(Σαβ)2(Σαβ)2⇒(−7)4=α2β2+β2γ2+γ2α2+2αβγ(α+β+γ)α2β2+β2γ2+γ2α2+2αβγ(α+β+γ)=α2β2+β2γ2+γ2α2α2β2+β2γ2+γ2α2[∵Σα=α+β+γ=0]=α4β4+β4γ4+γ4α4+2α4β2γ2+2α2β4γ2+2α2β2γ4=Σα4β4+2α2β2γ2α2+β2+γ2=Σα4β4+2α2β2γ2(Σα)2−2Σαβ=Σα4β4+2α2β2γ2[0−2×(−7)]=Σα4β4+2(−7)2(2×7)⇒ Σα4β4=(−7)4+4(−7)3⇒ Σα4β4=(−7)3(−7+4)=−3(−7)3On putting this value in Eq. (i), we get1α4+1β4+1γ4=−3(−7)3(−7)4=−3−7=37 Related content Oppositional Defiant Disorders Good Friday Wishes CBSE Class 9 Physics Motion Worksheet Autism Spectrum Disorder Sine and Cosine Waves Hindu Festivals List 2024 JEE Main Eligibility Criteria 2024 Session 2 (Released), Age Limits, Qualifying Marks, and Important Factor MCQs on Plant Hormones Class 10 5 Reasons To Choose The Commerce Stream After 10th Fl Words