已知X=根号3-根号2,求X的6次方+2倍根号2乘以X的5次方-X的4次方+X的3次方-2倍根号3乘以X的2次方+2X+
4个回答

利用(根号3+根号2)乘以(根号3-根号2)=1来化简

X的6次方+2倍根号2乘以X的5次方-X的4次方+X的3次方-2倍根号3乘以X的2次方+2X+根号2

= (X的6次方+2倍根号2乘以X的5次方-X的4次方)+(X的3次方-2倍根号3乘以X的2次方+2X+根号2)

=[ (X +2倍根号2)乘以X的5次方-X的4次方]+[(X -2倍根号3)乘以X的2次方+2X+根号2]

=[ (根号3+根号2)乘以X的5次方-X的4次方]+[-(根号3+根号2)乘以X的2次方+2X+根号2]

=[(根号3+根号2)乘以X乘以X的4次方-X的4次方]+ [-(根号3+根号2)乘以X乘以X+2X+根号2]

=[(根号3+根号2)乘以(根号3-根号2)乘以X的4次方-X的4次方]+ [-(根号3+根号2)乘以(根号3-根号2)乘以X+2X+根号2]

=(X的4次方-X的4次方)+(-X+2X+根号2)

=0+(X+根号2)

=根号3