Consider the following simultaneous equations in x and y: x + y + a x...
Consider the following simultaneous equations in and :
where is a real constant. Show that these equations admit real solutions in and .
Answer & Explanation
Eliminating one of the two unknowns, say we can form a Cubic equation in
Using Complex conjugate root theorem, an odd degree equation with real coefficients has an odd number of (at least one) real root(s)
From the first equation given, if is real so will be and vice versa