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Question Number 52592 by tanmay.chaudhury50@gmail.com last updated on 10/Jan/19

if x+y+z=1  x^2 +y^2 +z^2 =2  x^3 +y^3 +z^3 =3  find x^4 +y^4 +z^4

ifx+y+z=1x2+y2+z2=2x3+y3+z3=3findx4+y4+z4

Answered by math1967 last updated on 10/Jan/19

x+y+z=1  ⇒2(xy+yz+zx)=1−2=−1  ∴(xy+yz+zx)=−(1/2)  x^2 y^2 +y^2 z^2 +z^2 x^2 +2xyz(x+y+z)=(1/4)  x^2 y^2 +y^2 z^2 +z^2 x^2 =(1/4)−(1/3)=−(1/(12)) ★  x^3 +y^3 +z^3 −3xyz+3xyz=3★  (x+y+z)(x^2 +y^2 +z^2 −xy−yz−zx)+3xyz=3  3xyz=3−(5/2)=(1/2)⇒xyz=(1/6)  (x^2 +y^2 +z^2 )^2 =4  x^4 +y^4 +z^4 +2(x^2 y^2 +y^2 z^2 +z^2 x^2 )=4  x^4 +y^4 +z^4 =4+(1/6)=4(1/6)ans

x+y+z=12(xy+yz+zx)=12=1(xy+yz+zx)=12x2y2+y2z2+z2x2+2xyz(x+y+z)=14x2y2+y2z2+z2x2=1413=112x3+y3+z33xyz+3xyz=3(x+y+z)(x2+y2+z2xyyzzx)+3xyz=33xyz=352=12xyz=16(x2+y2+z2)2=4x4+y4+z4+2(x2y2+y2z2+z2x2)=4x4+y4+z4=4+16=416ans

Commented by tanmay.chaudhury50@gmail.com last updated on 10/Jan/19

bah darun excellent...

bahdarunexcellent...

Commented by math1967 last updated on 10/Jan/19

dhanyabad

dhanyabad

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