sqrt(x)+y=31

x+sqrt(y)=41

2. Equation

Hello math123x
Originally Posted by math123x

sqrt(x)+y=31

x+sqrt(y)=41
If these equations are going to have exact solutions, $\displaystyle x$ and $\displaystyle y$ will have to be perfect squares. A little thought will show you that the only perfect squares that are about the right size are $\displaystyle 25$ and $\displaystyle 36$.

$\displaystyle x=36$ and $\displaystyle y = 25$ gives the solution. Just trial and error, I'm afraid.

The only other way would be to eliminate $\displaystyle x$, say, and solve the equation for $\displaystyle y$. But it's a quartic:

$\displaystyle y = (41 - (31-y)^2)^2$

and I don't like the look of it! (But you can check that $\displaystyle y = 25$ is a solution if you like!)

Hello math123xIf these equations are going to have exact solutions, $\displaystyle x$ and $\displaystyle y$ will have to be perfect squares. A little thought will show you that the only perfect squares that are about the right size are $\displaystyle 25$ and $\displaystyle 36$.

$\displaystyle x=36$ and $\displaystyle y = 25$ gives the solution. Just trial and error, I'm afraid.