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If x+y+z=6 ,x^2+y^2+z^=26 and x^3+y^3+z^3=90 . Then find value of (xyz)^2

If x+y+z=6 ,x^2+y^2+z^=26 and x^3+y^3+z^3=90 . Then find value of (xyz)^2

Grade:11

1 Answers

shashank
11 Points
6 years ago
x+y+z=6                                                                                          (i)
x2+y2+z2=26                                                                                   (ii)
x3+y3+z3=90                                                                                   (iii)
sqauring  equation (i) on both sides we get
x2+y2+z2+2(xy+yz+zx)=36
26+2(xy+yz+zx)=36                                                                        (using ii)
xy+yz+zx=5                                                                                    (iv)
x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx)
90-3xyz=(6)(26-5)                                                                           (using i,ii,iii and iv)
xyz=-12
(xyz)2=144
 
 
 

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