arithmetic mean and geometric mean

$GM=\sqrt{xy}$ $\color{#D61F06}\implies$ $20=\sqrt{xy}$ $\color{#D61F06}\implies$ $400=xy$ $\boxed{1}$

$AM=\dfrac{x+y}{2}$ $\color{#D61F06}\implies$ $25=\dfrac{x+y}{2}$ $\color{#D61F06}\implies$ $50=x+y$ $\color{#D61F06}\implies$ $y=50-x$ $\boxed{2}$

Substitute $\boxed{2}$ in $\boxed{1}$ ,

$400=x(50-x)$ $\color{#D61F06}\implies$ $400=50x-x^2$ $\color{#D61F06}\implies$ $x^2-50x+400=0$ $\color{#D61F06}\implies$ $(x-10)(x-40)=40$ $\color{#D61F06}\implies$ $x=10~or~x=40$

The desired answer is $x=10$ .