Question 68
(a) Verify the identity
$$(a+b+c)^3=a^3+b^3+c^3+3(a+b)(b+c)(c+a).$$
(b) Solve the system
$$\begin{cases}x+y+z=1,\\x^2+y^2+z^2=1,\\x^3+y^3+z^3=1.\end{cases}$$
$$(a+b+c)^3=a^3+b^3+c^3+3(a+b)(b+c)(c+a).$$
(b) Solve the system
$$\begin{cases}x+y+z=1,\\x^2+y^2+z^2=1,\\x^3+y^3+z^3=1.\end{cases}$$