Question

已知x=4-根号3，求x四次方-6x三次方-2x²+18x+23的值

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Answer 1

x-4=-√3
平方
x²-8x+16=3
x²-8x=-13

原式=x^4-8x³+2x³-2x²+18x+23
=x²(x²-8x)+2x³-2x²+18x+23
=-13x²+2x³-2x²+18x+23
=2x³-16x²+x²+18x+23
=2x(x²-8x)+x²+18x+23
=2×(-13)x+x²+18x+23
=x²-8x+23
=-13+23
=10