Question

已知x-y=1,x的立方-y的立方=2,求x四次方+y四次方及 x 的5次方 -y的5次方 的值是

Answer 1

x-y=1 平方一下x^2-2xy+y^2=1 1x^3-y^3=(x-y)(x^2+xy+y^2)=x^2+xy+y^2=2 21式+2式得x^2+y^2=3/2 32式-1式得xy=1/4 43式平方得x^4+2x^2y^2+y^4=9/4x^4+y^4=9/4-2(xy)^2=9/4-2*(1/4)^2=17/8(x^4+y^4)(x-y)=x^5-x^4y+xy...