Question

aratati ca 29 la puterea 2001 se poate scrie ca o suma de 3 patrate perfecte​

Answer 1

 

$\displaystyle\bf\\Explicatie:\\Folosim~propr.~lui~29~de~a~fi~scris~ca~suma~de~3~patrate~perfecte.\\\\29=4+9+16=2^2+3^2+4^2\\\\Rezolvare:\\\\29^{2001}=29^{2000+1}=29^{2000}\times29=29^{2000}\Big(4+9+16\Big)=\\\\=29^{2000}\times4+29^{2000}\times9+29^{2000}\times16=\\\\=29^{1000\times2}\times2^2+29^{1000\times2}\times3^2+29^{1000\times2}\times4^2=\\\\=\Big(29^{1000}\Big)^2\times2^2+\Big(29^{1000}\Big)^2\times3^2+\Big(29^{1000}\Big)^2\times4^2=$

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$\displaystyle\bf\\=\Big(29^{1000}\times2\Big)^2+\Big(29^{1000}\times3\Big)^2+\Big(29^{1000}\times4\Big)^2\\\\Asta~este~suma~de~3~patrate~perfecte.$