<prompt> Acha x iwe nambari halisi chanya. Pata thamani ya juu iwezekanavyo ya fracx22-sqrtx44x.  <response>: Kurekebisha nambari, tunapataanzaalignfracx22-sqrtx44xcdotfracx22sqrtx44x22 sqrtx44fracx222-x44xx22sqrtx44 frac4x2xx22sqrtx44frac4frac1xx22sqrtx44frac4xfrac2xsqrtx2frac4x2.endalignKwa kuwa tunataka kuongeza idadi hii, tungependa kupunguza kipunguzo. Na AM-GM, xfrac2xgeq 2sqrt2 na x2frac4x2geq 4, ili kipunguzi kiwe angalau 2sqrt22. Kwa hivyo, fracx22-sqrtx44xleq frac42sqrt222sqrt2 -2,na usawa wakati xsqrt2. 