※ 引述《annzi (打桌球)》之銘言：
: a,b,c 為 x^3 + x - 1=0 之三根 求a^5 +b^5 +c^5=? ans:-5
: 謝謝
a + b + c = 0
ab + bc + ca = 1
abc = -1
=>a^2 + b^2 + c^2=( a + b + c )^2 - 2(ab + bc + ca) = -2
and x^3 + x - 1 = 0
=> x^3 = -x + 1 => x^5 = x^2( -x + 1 ) = x^2 + x -1
hence a^5 +b^5 +c^5 = ( a^2 + a -1 ) + ( b^2 + b -1 ) + ( c^2 + c -1 )
=( a^2 + b^2 + c^2 ) + ( a + b + c ) -3 = -5
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