solution to last prob.

well from the Cauchy inequality we have
(a+b+c+d)( 1/a + 1/b + 1/c +1/d) => (1+1+1+1)^2=16

well for this we get

(a+b+c+d)( 1/a + 1/b + 4/c + 16/d) => (1+1+2+4)^2=64. so we are done.