Question

已知X平方+X-8=0 求代数式X五次方+2X四次方+3X三次方+4X平方-87X+1值

Answer 1

X^2+X-8=0

X^2+X=8

X=(-1±根号33)/2

X^5+2X^4+3X^3+4X^2-87X+1

= X^5+X^4+X^4+X^3+2X^3+4X^2-87X+1

=X^3 (X^2+X) + X^2(x^2+x)+2X^3+4X^2-87X+1

=8X^3 + 8X^2 + 2X^3 + 4X^2 - 87X + 1

=10X^3 + 12X^2 - 87X + 1

=10X^3 +10X^2+ 2X^2 + 2X - 89X + 1

=10X (X^2 +X) + 2(X^2 + X) - 89X + 1

=80X + 16 - 89X + 1

=17 - 9X

=17-9(-1±根号33)/2

=(43±根号33)/2