X2²+X1X2+X1²如何变成(X2+X1/2)²+3/4*X1²?
问题描述:
X2²+X1X2+X1²如何变成(X2+X1/2)²+3/4*X1²?
答
用y表示X1,用x表示X2
x²+xy+y²=x²+2(y/2)x+(y/2)²-(y/2)²+y²
=(x+y/2)²+(y²-y²/4)
=(x+y/2)²+3/4y²
答
x1²+x1x2+x2²
=[x1²+x1x2+(1/4)x2²]+(3/4)x2²
=[x1+(1/2)x2]²+(3/4)x2²
答
X2²+X1X2+X1²
=X2²+X1X2+1/4X1²+3/4X1²
=(X2+X1/2)²+3/4*X1²
答
X2²+X1X2+X1²
=(X2²+X1X2+1/4*X1²)+3/4*X1²
=(X2+X1/2)²+3/4*X1²