wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

if x+y+z=1 and xy +yz + zx =-1 and xyz = -1 then find x³+y³+z³

Open in App
Solution

Use the algebraic formula. x3+y3+z3-3xyz=x+y+z x2+y2+z2-xy-yz-zxThis implies that, x3+y3+z3=x+y+z x2+y2+z2-xy+yz+zx+3xyz ....1We know the algebraic formula. x+y+z2=x2+y2+z2+2xy+2yz+2zxThis gives, x2+y2+z2= x+y+z2-2xy+yz+zxSince x+y+z=1, xy+yz+zx=-1, we get x2+y2+z2= 12-2-1 = 1+2 =3 Then from 1, we get x3+y3+z3=1 3--1+3-1 =1 3+1-3 =1 4-3 =4-3 =1

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Introduction to Fundamental Concepts
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon