The roots of the eqn x^4  3x^2 + 5x  2 = 0 are a, b, c, d, and a^n + b^n + c^n + d^n is denoted by S~n. The equation of the roots a^2, b^2, c^2, d^2 is y^4  6y^3 + 5y^2  13y + 4 = 0. State the value of S~2 and hence show that S~8 = 6S~6  5S~4 + 62.
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