# Math Help - Solving equation, please help....

1. ## Solving equation, please help....

I am in great fix, please help in solving these equations... I want to know how to solve it, thanks in advance.....

sqrt(x)+y=31

x+sqrt(y)=41

2. ## Equation

Hello math123x
Originally Posted by math123x
I am in great fix, please help in solving these equations... I want to know how to solve it, thanks in advance.....

sqrt(x)+y=31

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

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

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

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

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

Grandad

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

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

Grandad
This is the only problem. I git thid in a competetion, where i have to tell how we solved this question; Analytical part will not work up.

And here in this case we have small no like 31 and 41, so it is still easy to find solution, but what if we go bigger/ greater no(s) like 1000 or even more....

4. In that case go ahead to solve that equation (cursing your luck) and when you get that fourth degree equation, try solving it using by this method

Thanks to Hallsofivy for that