Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 200622 by sonukgindia last updated on 21/Nov/23

Answered by Rasheed.Sindhi last updated on 21/Nov/23

•(a+b+c)^2 =4^2 =16 a^2 +b^2 +c^2 +2(ab+bc+ca)=16 ab+bc+ca=((16−10)/2)=3 •a^3 +b^3 +c^3 −3abc=(a+b+c)(a^2 +b^2 +c^2 −(ab+bc+ca)) 22−3abc=(4)(10−3)=28 abc=((22−28)/3)=−2 •(ab+bc+ca)^2 =3^2 =9 a^2 b^2 +b^2 c^2 +c^2 a^2 +2abc(a+b+c)=9 a^2 b^2 +b^2 c^2 +c^2 a^2 +2(−2)(4)=9 a^2 b^2 +b^2 c^2 +c^2 a^2 =9+16=25 •(a^2 +b^2 +c^2 )^2 =10^2 =100 a^4 +b^4 +c^4 +2(a^2 b^2 +b^2 c^2 +c^2 a^2 )=100 a^4 +b^4 +c^4 +2(25)=100 a^4 +b^4 +c^4 =100−50=50

∙(a+b+c)2=42=16a2+b2+c2+2(ab+bc+ca)=16ab+bc+ca=16−102=3∙a3+b3+c3−3abc=(a+b+c)(a2+b2+c2−(ab+bc+ca))22−3abc=(4)(10−3)=28abc=22−283=−2∙(ab+bc+ca)2=32=9a2b2+b2c2+c2a2+2abc(a+b+c)=9a2b2+b2c2+c2a2+2(−2)(4)=9a2b2+b2c2+c2a2=9+16=25∙(a2+b2+c2)2=102=100a4+b4+c4+2(a2b2+b2c2+c2a2)=100a4+b4+c4+2(25)=100a4+b4+c4=100−50=50

Answered by mr W last updated on 21/Nov/23

p_1 =e_1 =4 p_2 =e_1 p_1 −2e_2 =4×4−2e_2 =10 ⇒e_2 =3 p_3 =e_1 p_2 −e_2 p_1 +3e_3 =4×10−3×4+3e_3 =22 ⇒e_3 =−2 p_4 =e_1 p_3 −e_2 p_2 +e_3 p_1 =4×22−3×10−2×4=50 i.e. a^4 +b^4 +c^4 =50 ✓ generally we have p_n =4p_(n−1) −3p_(n−2) −2p_(n−3) p_n =a^n +b^n +c^n =2^n +(1+(√2))^n +(1−(√2))^n

p1=e1=4p2=e1p1−2e2=4×4−2e2=10⇒e2=3p3=e1p2−e2p1+3e3=4×10−3×4+3e3=22⇒e3=−2p4=e1p3−e2p2+e3p1=4×22−3×10−2×4=50i.e.a4+b4+c4=50✓generallywehavepn=4pn−1−3pn−2−2pn−3pn=an+bn+cn=2n+(1+2)n+(1−2)n

Terms of Service

Privacy Policy

Contact: info@tinkutara.com