A Nice Math Olympiad Radical Problem

A Nice Math Olympiad Radical Problem

[quixata]

Note that, the given expression involving 'a' is symmetric in 'a' and thus, if 'k' is a root if the equation then '-k' is another root.

sqrt(a) + sqrt(-a) = 12
=> sqrt(a) + i*sqrt(a) = 12
=> sqrt(a) * (1 + i) = 12
Squaring both sides,
=> 2ia = 144
=> a = 72/i = -72i
So, a = 72i is another solution.
Ans. a = + or - 72i

Note: To get the positive root analytically, in the LHS, take common sqrt(-a)

[MansorMohammed-kr]

au départ dire résoudre dans dans l ensemble C