Question: For a, b, c three real numbers consider the system x + ax + ax + ax3 = a + bx + bx +

$For ( a, b, c ) three real num bers consider the system [ begin{aligned} x_{0}+a x_{1}+a^{2} x_{2}+a^{3} x_{3} & =a^{4}$ (b) Solve the system for ( (a, b, c)=(0,1,-1) ).

For a, b, c three real numbers consider the system x + ax + ax + ax3 = a + bx + bx + b x3 = 64 x + cx + x + c x3 = x (a) Without solving the system, show that it can never have a unique solution for any value of a, b and c. (b) Solve the system for (a, b, c) = (0, 1, -1).

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