Question

(97^3-53^3/44+97*53):(153,5^2-27,5^2)
Пожалуйста, побыстрее и с объяснением!

Answer 1

$\displaystyle\bf\\\Bigg(\frac{97^{3}-53^{3} }{44} +97\cdot 53\Bigg):\Big(152,5^{2} -27,5^{2} \Big)=\\\\\\=\Bigg(\frac{(97-53)\cdot(97^{2} +97\cdot 53+53^{2} )}{44} +97\cdot53\Bigg):\\\\\\:\Bigg[(152,5-27,5)\cdot(152,5+27,5\Big)\Bigg]=\\\\\\=\Bigg(\frac{44\cdot(97^{2} +97\cdot 53+53^{2} )}{44} +97\cdot 53\Bigg):\Big(125\cdot 180\Big)=\\\\\\=\Big(97^{2} +97\cdot 53+53^{2} +97\cdot 53\Big):\Big(125\cdot 180\Big)=$

$\displaystyle\bf\\=\frac{97^{2} +2\cdot 97\cdot 53+53^{2} }{125\cdot 180} =\frac{(97+53)^{2} }{125\cdot 180} =\frac{150^{2} }{125\cdot 180} =\\\\\\=\frac{25\cdot 25\cdot 36}{25\cdot 5\cdot 5\cdot 36} =1$