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 CBSE Class 10 Grading System and Marking Scheme 2024 Vocabulary Words For IELTS List, Preparation Tips Science GK Quiz in Hindi : जानिए विज्ञान से जुड़े महत्वपूर्ण सामान्य ज्ञान UP Board Class 10 Result 2024 Out Check Your Result How to Study for NEET from Class 8? Do or Die Chapters For NEET 2024 List of Phobias: Common Phobias From A to Z JEE Main 2024 April 6 Question Paper and Answer Key PDF with Solutions- Shift 1, 2 NEET MDS 2024 Result by April 18, Check Expected Cutoff Letter to Your Friend Describing Your Ancestral House