GATE Electronics and Communications (EC) 2018 Solved Paper

In the circuit shown below, the (𝑊/𝐿) value for M₂ is twice that for M₁. The two nMOS transistors are otherwise identical. The threshold voltage 𝑉_𝑇 for both transistors is 1.0V. Find V_x. 
Note that 𝑉_𝐺𝑆 for M₂ must be > 1.0 V.

Current through the NMOS transistors can be modelled as
${\mathit{I}}_{\mathit{D}\mathit{S}}=\mathit{\mu }{\mathit{C}}_{\mathit{o}\mathit{x}}\left(\frac{\mathit{W}}{\mathit{L}}\right)\left(\left({\mathit{V}}_{\mathit{G}\mathit{S}}-{\mathit{V}}_{\mathit{T}}\right){\mathit{V}}_{\mathit{D}\mathit{S}}-\frac{1}{2}{\mathit{V}}_{\mathit{D}\mathit{S}}^2\right)\mathit{f}\mathit{o}\mathit{r}{\mathit{V}}_{\mathit{D}\mathit{S}}\le {\mathit{V}}_{\mathit{G}\mathit{S}}-{\mathit{V}}_{\mathit{T}}$
${\mathit{I}}_{\mathit{D}\mathit{S}}=\mathit{\mu }{\mathit{C}}_{\mathit{o}\mathit{x}}\left(\frac{\mathit{W}}{\mathit{L}}\right)\frac{\left({\mathit{V}}_{\mathit{G}\mathit{S}}-{\mathit{V}}_{\mathit{T}}\right){}^2}{2}\mathit{f}\mathit{o}\mathit{r}{\mathit{V}}_{\mathit{D}\mathit{S}}\ge {\mathit{V}}_{\mathit{G}\mathit{s}}-{\mathit{V}}_{\mathit{T}}$