`ME^2 + MC^2 + CE^2 = 2MC^2 + CE^2`
Ta có : `MC^2 = MF^2 + CF^2 = (a + x/2)^2` + $\frac{4a^2 - x^2}{4}$
`<=> MC^2 = a^2 + ax + x^2/4 + a^2 - x^2/4`
`<=> MC^2 = 2a^2 + ax`
`CE^2 = 4a^2 - x^2`
`=> ME^2 + MC^2 + CE^2 = 4a^2 + 2ax + 4a^2 - x^2 = 8a^2 + 2ax - x^2`
`<=> ME^2 + MC^2 + CE^2 = 9a^2 - (x-a)^2`
Để `ME^2 + MC^2 + CE^2` max thì `(x-a)^2` min `=0` `<=> x = a`
Vậy `ME^2 + MC^2 + CE^2` max `<=> x = a`