已知x等于2减根号3 求x的4次方加6x的平方减5x的3次方减5x的值
问题描述:
已知x等于2减根号3 求x的4次方加6x的平方减5x的3次方减5x的值
答
x=2-根号3
2-x=根号3
两遍平方
x^2-4x+4=3
x^2=4x-1
x^4+6x^2-5x^3-5x
=(4x-1)^2+6x^2-5x(4x-1)-5x
=16x^2-8x+1+6x^2-20x^2+5x-5x
=2x^2-8x+1
=2(4x-1)-8x+1
=8x-2-8x+1
=-1