已知x=4-根号3,求x四次方-6x三次方-2x²+18x+23的值尽快回答啊.
问题描述：
已知x=4-根号3,求x四次方-6x三次方-2x²+18x+23的值
尽快回答啊.
答
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