the first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

Expansion of (x+y)ⁿ upto 3 term
​$n_{C_0}{x}^n+n_{C_1}{x}^{n-1}y+n_{C_2}{x}^{n-2}{y}^2+......$
So we are given
$$\begin{gathered} n_{C_0} x^n=1 \\ \Rightarrow x^n=1 ......................... \left(i\right) \end{gathered}$$ 
and

$$\begin{gathered} n_{C_1}{x}^{n-1}y=56 \\ \Rightarrow n{x}^{n-1}y=56 \\ \Rightarrow n{x}^{{}^n}\frac{y}{x}=56 \\ \Rightarrow \frac{ny}{x}=56 .......................................\left(ii\right) \end{gathered}$$
$$\begin{gathered} n_{C_2}{x}^{n-2}{y}^2=1372 \\ \Rightarrow \frac{n(n-1)x^n{y}^2}{2x^2}=1372 \\ \Rightarrow \frac{n(n-1)y^2}{2x^2}=1372 \\ \Rightarrow \frac{n(n-1)}{2}\frac{{56}^2}{n^2}=1372 from 2nd equation \\ \Rightarrow 1568(n-1)=1372n \\ \Rightarrow 1568n-1372n=1568 \\ \Rightarrow 196n=1568 \\ \Rightarrow n=8 \end{gathered}$$
From equation (i) we have
$$\begin{gathered} x^n=1 \\ \Rightarrow x^8=1 \\ \Rightarrow x=1 \end{gathered}$$
From equation(ii) we have
$$\begin{gathered} \frac{ny}{x}=56 \\ \Rightarrow 8y=56 \\ \Rightarrow y=7 \end{gathered}$$
So x=1, y =7, n=8