X2²+X1X2+X1²如何变成(X2+X1/2)²+3/4*X1²?

X2²+X1X2+X1²如何变成(X2+X1/2)²+3/4*X1²?
X2²+X1X2+X1²如何变成(X2+X1/2)²+3/4*X1²?

X2²+X1X2+X1²如何变成(X2+X1/2)²+3/4*X1²?
X2²+X1X2+X1²
=X2²+X1X2+1/4X1²+3/4X1²
=(X2+X1/2)²+3/4*X1²

X2²+X1X2+X1²
=(X2²+X1X2+1/4*X1²)+3/4*X1²
=(X2+X1/2)²+3/4*X1²

x1²＋x1x2＋x2²
=[x1²＋x1x2＋(1/4)x2²]＋(3/4)x2²
=[x1＋(1/2)x2]²＋(3/4)x2²

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