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- Feb 14, 2012
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Let \(\displaystyle a\), \(\displaystyle b\), \(\displaystyle c\) and \(\displaystyle d\) be positive real numbers such that
\(\displaystyle a^2+b^2+(a-b)^2=c^2+d^2+(c-d)^2\).
Prove that
\(\displaystyle a^4+b^4+(a-b)^4=c^4+d^4+(c-d)^4\).
\(\displaystyle a^2+b^2+(a-b)^2=c^2+d^2+(c-d)^2\).
Prove that
\(\displaystyle a^4+b^4+(a-b)^4=c^4+d^4+(c-d)^4\).