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1.x-z=x-y-z+y=a-10
x²+y²+z²-xy-yz-zx
=1/2(2x²+2y²+2z²-2xy-2yz-2zx)=0
即x²-2xy+y²+y²-2yz+z²+x²-2zx+z²
=1/2[(x-y)²+(y-z)²+(x-z)²]
=1/2[(a-10)^2+100+a^2]
=a^2-10a+100
=(a-5)^2+75
当a=5时 最小值为75

2.运用x²=2x+2代入所求式子 碰到x^2就用2x+2代换
x^4-4x^3+6x^2-4x+3
=(2x+2)^2-4x(2x+2)+6x^2-4x+3
=4x^2+8x+4-8x^2-8x+6x^2-4x+3
=2x^2-4x+7
=2(2x+2)-4x+7
=4x+4-4x+7
=11

3.令a/2=b/3=c/4=k
a=2k
b=3k
c=4k
(2a²-3bc+b²)/(a²-2ab-c²)
=(4*2-3*3+16)k^2/(4-2*2*3-4*4)k^2
=1/2

第一题=x(x-y)-y(z-y)+z(z-x)
=ax-10y+(10-a)z
=ax-10y+10z-az
=10(z-y)_a(z-x)
=10*10-a(10-a)
=100-10a+a的平方
=(a-5)的平方+75
a=5时,最小值是75
第二题
=x的四次方-2x的三次方-2x的三次方+4x的平方-4x+3
=x的平方x(x-2)-2xx(x-2)+2x(x-2)+3
带入已知x(x-2)=2
=2x的平方-4x+4+3
=2x(x-2)