已知A=3x2-xy+y2,B=2x2-3xy+2y2,其中x,y满足等式2(x-1/2)2+∣y-1∣=0,求3B-2A的值.儿子问呢,

问题描述:

已知A=3x2-xy+y2,B=2x2-3xy+2y2,其中x,y满足等式2(x-1/2)2+∣y-1∣=0,求3B-2A的值.
儿子问呢,

2(x-1/2)²+∣y-1∣=0,
则x-1/2=0
y-1=0
解得x=1/2
y=1
则A=3x2-xy+y2=3*(1/2)²-(1/2)*1+1²=3/4-1/2+1=5/4
B=2x2-3xy+2y2=2*(1/2)²-3*(1/2)*1+2*1²=1/2-3/2+2=1
所以3B-2A
=3*1-2*(5/4)
=3-5/2
=1/2