Hi,
My question is how do you solve analitically:
sqrt(x)+y=7 and sqrt(y)+x=11 without solving a 4th degree polynomial equation?
Thanks
Dear kolg,
------------(1)
-------------(2)
From (1); y<11 and
From (2); x<7 and
Therefore, and
Also from (1) and (2) it could be seen that, and
Therefore x=4 is the only solution for x.
When,
Therefore x=4, y=9 is the only solution for this system of equations.
Dear Klog,
If is rational but not an integer,
where
Therefore,
Hence is irrational.
Then is irrational. (Contradiction)
Therefore is irrational or an integer.(according to our assumption.)
But if is irrational is irrational. (Contradiction)
So is an integer.
Same proof goes to as well.
Hope this helps.