Question

已知x=（根号2+1）/2,求代数式4x的平方+4x的三次方-9x的平方-2x+1的值

Answer 1

x=(根号2+1)/2

根号2=2x-1

两边平方

(2x-1)^2=2

4x^2-4x+1=2

4x^2-4x=1

4x^4+4x^3-9x^2-2x+1

=4x^4-4x^3+8x^3-9x^2-2x+1=x^2(4x^2-4x)+8x^3-9x^2-2x+1

=x^2*1+8x^3-9x^2-2x+1

=8x^3-8x^2-2x+1

=2x(4x^2-4x)-2x+1

=2x*1-2x+1

=1