The simultaneous equations {x^2+2y^2=6 have two equal real solutions
mx+y=3

(a)Find the value(s) of m
(b)Solve the simultaneous equations

謝解答

Part (a)
y = 3 - mx

Put that into x^2 + 2y^2 = 6, you have

(m^2+1)x^2 - 12mx + 12 = 0

Since two roots are equal, determinant = 0
96m^2 - 48 = 0

Part (b) just put value of m into the equation and solve it