152 4. Equations
- x+y+z=3a
x2+y2+z2= 14+2a+5a2
xyz = 6 - lOa - 4a2. - a(y - z) + b(z - x) + c(x - y) = 0
(x - y)(y - z)(z - x) = d3
x+y+z=e. - x(y + z)~ = 1 + a3
x+y=3/2+z
yz = 3116. - x2 + 2xy - y2 = ax + by
x2 - 2xy - y2 = bx - ay (a, b are real constants). - x2 + w2 + v2 = a2 VW + u(y + z) = bc
w2 + y2 + u2 = b2 wu + v(z + x) = ca
v2 + u2 + .z2 = c2 UZI + w(x + y) = ab
(a, b, c are positive reals; x, y, Z, u, V, w to be real). - u + 21 = a
ux+vy=b
‘11x2 + vy2 = c
ux3 + vy3 = d (a, b, c, d are nonzero constants). - x+y+r=5
x2 + y2 + 22 = 9
xy+u+vx+vy=o
yz + u + vy + vz = 0
%X + u + vz + VX = 0. - by + cz = (y - z)”
cz + ax = (z - x)~
ax + by = (x - Y)~.
20.
(ab + 1)(x2 + 1) = (a2 + l)(xy + 1)
(x + 1) (Y + 1)
Cab + l)(y2 + 1) = (b2 + l)(xy + 1)
(Y + 1) (x+1) *- x3+y3+z3=8