# non linear system of equations leading to quartic

The question asks to solve the system

$$\begin{cases} \sqrt x + y = 16 \\ \sqrt y + x = 25 \end{cases}$$

Substitution leads to a fourth degree polynomial.

Is there n easier way to solve it ?

Thanks.

• The solution looks terrible, i think there is no other way. – Dr. Sonnhard Graubner Apr 26 '19 at 5:25
• If you plug it into Alpha it finds a very messy solution. When you ask for a numeric answer it can't even tell it is real. – Ross Millikan Apr 26 '19 at 13:48

• Nice extras! ${}$ – Jyrki Lahtonen May 3 '19 at 7:08