⒈X+Y=4,X^2-Y^2=20则X=Y=⒉X^3-6X^2+11X-6=(X-1)(X^2+MX+N)求M、N

Question

⒈X+Y=4,X^2-Y^2=20
则X=___ Y=___
⒉X^3-6X^2+11X-6=(X-1)(X^2+MX+N)
求M、N

Answer 1

⒈X+Y=4,X^2-Y^2=20 ,
X+Y=4,(1)
(X+Y)(X-Y)=20,(2)
把(1)代入(2)得X-Y=5,(3)
(1)+(2)得2X=9,
所以X=4.5,
所以Y=-0.5;
⒉X^3-6X^2+11X-6=(X-1)(X^2+MX+N)=X^3+(M-1)X^2+(N-M)X-N,
所以M-1=-6,
N-M=11,
-N=-6,
所以N=6,M=-5.