Show that equations $($B$)$ and $($C$)$ combine in accord with the equation M $=$ixiM$$i

to regenerate equation $($A$).$The enthalpy of a binary liquid system of species $1$ and $2$ at fixed $T$ and $P$ is represented by the equation

$H=400x_1+600x_2+x_1{x}_2(40x_1+20x_2)$

where $H$ is in $J*mo{l}^{-1}.$ The partial enthalpies are

$\frac{?}{\text{b}\text{a}\text{r}}(H{)}_1=420-60x_1^2+40x_1^3\frac{?}{b}$

$ar(H{)}_2=600+40x_1^3$