Consider the following simultaneous equations in x and y: x + y + a x...

skylsn

skylsn

Answered

2022-06-30

Consider the following simultaneous equations in x and y:
x + y + a x y = a
x 2 y x y 2 = 0
where a is a real constant. Show that these equations admit real solutions in x and y.

Answer & Explanation

Govorei9b

Govorei9b

Expert

2022-07-01Added 21 answers

Eliminating one of the two unknowns, say y we can form a Cubic equation in x
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 x is real so will be y and vice versa

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