If a^2 x^3+b^2 y^3+c^2 z^3=1024, ax^2=by^2=cz^2 and 1/x+1/y+1/z=1/4, find the value of (√a+√b+√c).

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x_1,x_2,x_3 are roots of x^3-x^2+4=0, find |(x_1+〖x_2〗^2+〖x_3〗^2 )(x_2+〖x_3〗^2+.+〖x_1〗^2+〖x_2〗^2 )|.x_1,x_2,x_3 are roots of x^3-x^2+4=0, find |(x_1+〖x_2〗^2+〖x_3〗^2 )(x_2+〖x_3〗^2+.+〖x_1〗^2+〖x_2〗^2 )|.
If x^2+y^2+2xy+yz+zx=66, y^2+z^2+2yz+zx+xy=99 and z^2+x^2+2zx+xy+yz=77, find value of x^2+y^2+z^2.If x^2+y^2+2xy+yz+zx=66, y^2+z^2+2yz+zx+xy=99 and z^2+x^2+2zx+xy+yz=77, find value of x^2+y^2+z^2.