Question

1．若3X平方减X等于1,求6X立方加7X平方减5X加1990的值?

Answer 1

1.
原式=6x^3+7x^2-5x+1990
=2x(3x^2-x)+3(3x^2-x)-2x+1990
=2x+3-2x+1990
=1993
2.
(x-1)^3+(y-1)^3+(z-1)^3=0
=> (x+y-2)[(x-1)^2-(x-1)(y-1)+(y-1)^2]+(z-1)^3=0
=> (1-z)[(x-1)^2-(x-1)(y-1)+(y-1)^2]+(z-1)^3=0
=> (z-1)*[(z-1)^2-(x-1)^2+(x-1)(y-1)-(y-1)^2]=0
所以
z=1或者(z-1)^2-(x-1)^2+(x-1)(y-1)-(y-1)^2=0
所以x,y,z中至少一个等于1.
4.
x^3-5x+4
=x^3-x-4x+4
=x(x+1)(x-1)-4(x-1)
=(x-1)(x^2+x-4)