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
Rajat Meshram , 9 Years ago
Grade 11
10 grade maths> If x+y+z=6 ,x^2+y^2+z^=26 and x^3+y^3+z^3...
1 Answersshashank
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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