If #x=a+b,y=aw+bw^2,z=aw^2+bw# then find #x^2+y^2+z^2 and xyz#?

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Answer 1 · 2018-08-13T00:42:01

#x^2+y^2+z^2#

#=a^2(1+w^2+w^4)+2ab(1+w^3+w^3)+b^2(1+w^4+w^2)#

#=a^2(1+w^2+w)+2ab(1+1+1)+b^2(1+w+w^2)#

#=a^2xx0+2abxx3+b^2xx0#

#=6ab#

#xyz#

#=(a+b)(aw+bw^2)(aw^2+bw)#

#=(a^2w+abw+abw^2+b^2w^2)(aw^2+bw)#
#=(a^2w-ab+b^2w^2)(aw^2+bw)#

#=(a^3w^3-a^2bw^2+ab^2w^4+a^2bw^2-ab^2w+b^3w^3)#

#=a^3+b^3#