Prove that if 0<a<1 and 0<b<1 then
![\frac{ {a}^{2} + {b}^{2} }{2} > { (\frac{a + b}{2}) }^{2} \frac{ {a}^{2} + {b}^{2} }{2} > { (\frac{a + b}{2}) }^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B+%7Ba%7D%5E%7B2%7D+%2B+%7Bb%7D%5E%7B2%7D+%7D%7B2%7D+%26gt%3B+%7B+%28%5Cfrac%7Ba+%2B+b%7D%7B2%7D%29+%7D%5E%7B2%7D)
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