Show that, if the roots of the equation \[x^3-5x^2+qx-8=0\] are in geometric progression, then \(q=10\).

If \(\alpha\), \(\beta\), \(\gamma\) are the roots of the equation \[x^3-x^2+4x+7=0,\] find the equation whose roots are \(\beta+\gamma\), \(\gamma+\alpha\), \(\alpha+\beta\).