5. (2010 Shangrao senior two test) it is known that F1 and F2 are the two focuses of hyperbola x * 2 / A * 2-y * 2 / b * 2 = 1 (a > 0, b > 0). Take the line F1F2 as the edge to make the regular triangle mf1f2. If the midpoint P of the edge MF1 is on the hyperbola, then the eccentricity of the hyperbola is ()

F1F2=2c
So m (0, √ 3C)
F1(-c,0)
Then p (- C / 2, √ 3C / 2)
So C & sup2; / 4A & sup2; - 3C & sup2; / 4B & sup2; = 1
b²c²-3a²c²=4a²b²
(c²-a²)c²-3a²c²=4a²(c²-a²)
c^4-a²c²-3a²c²=4a²c²-4a^4
c^4-8a²c²+4a^4=0
c²=(4±2√3)a²
c=(√3±1)a
c>a
So e = C / a = √ 3 + 1

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