Let \(a, b, c, d, e, f, g,\) and \(h\) be real numbers such that \(abcd = 4\) and \(efgh = 9.\) Find the minimum value of \((ae)^2 + (bf)^2 + (cg)^2 + (dh)^2.\)
If a = b = c = d = √2 and e = f = g = h = √3, then (ae)2 + (bf)2 + (cg)2 + (dh)2 = 24
Not sure I can prove this a minimum though!
