3.2-7

$\sqrt5(F_{i+2}-\phi^i)=\phi^i\cdot \phi^2-(1-\phi)^{i+2}-\sqrt5\phi^i$
$=\phi^i\cdot (1-\phi)^2-(1-\phi)^{i+2}=(1-\phi)^2\cdot (\phi^i-(1-\phi)^i)$
$\geq(1-\phi)^2\cdot (\phi^i-(\phi-1)^i)\geq0$