Question

已知X²-2X=2,求代数式X四次方-4X三次方+6X²-4X+3的值

Answer 1

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

x^4-4x^3+4x^2=4

所以x^4-4x^3+6x^2-4x+3

=(x^4-4x^3+4x^2)+2(x^2-2x)+3

=(x^2-2x)^2+2(x^2-2x)+3

=4+2*2+3

=11