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
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.
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!)
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....
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