# Simultaneous Equations with Roots

## -

### 28/09/2021Solve Simultaneously

$x+y=11$ $x+y=7$

-/|\-

### Solution:

The equations imply that $x,y>0$.
Both equations have integers of the RHS
implying $x,y,\sqrt{x},\sqrt{y}$ are elements of the integers
moreover $x,y$ are perfect squares
so $0 and $0.
So $x\in \left\{1,4\right\}$ and $y\in \left\{1,4,9\right\}$.
Therefore $x=4$ and $y=9$
Are there any other solutions?

-oOo-

^
Contact Michael Andrew Smith on 0 77 86 69 56 06 or via mike.smith@physics.org

Expires 1 Year After Update

Site by M.A. Smith.