已知x=5-2√6,求3x^4-28x^3-17x^2+2x-10
问题描述:
已知x=5-2√6,求3x^4-28x^3-17x^2+2x-10
答
x=5-2√6
∴x-5=-2√6
(x-5)²=(-2√6)²
x²-10x+25=24
x²-10x+1=0
3x^4-28x^3-17x^2+2x-10
=3x^4-30x³+3x²+2x³-20x²+2x-10
=3x²(x²-10x+1)+2x(x²-10x+1)-10
=0+0-10
=-10