Question

I think this problem will require later to solve a fourth degree equation. Is there any shorter method for this?

Answer 1

If \[\sqrt{m}+n=3\]and \[m+\sqrt{n}=5\] find the values of m and n.

Answer 2

Maybe, maybe not... have you done using using 'conventional' methods?

Answer 3

Just one 'using'... gah

Answer 4

<shrugs> let's see...
\[\Large n = 3- \sqrt m\]\[\Large m + \sqrt{3-\sqrt{m}}= 5\]\[\Large \sqrt{3-\sqrt m}= 5- m\]Squaring both sides\[\Large3-\sqrt m = m^2 -10m + 25\]\[\Large m^2 -10m + \sqrt m +22= 0\]

Answer 5

This looks highly unappealing...
\[\Large u = \sqrt m\]\[\Large u^4 -10u^2 + u + 22 = 0\]

Answer 6

Come on, bro, make your presence felt :D