Вычислите наиболее рациональным способом: (〖76〗^3+ 〖25〗^3)/101- 76•25 СРОЧНО. Created by ShnykovaTanya85. algebra-ru

101- 76•25 СРОЧНО...

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Ответ:

$\dfrac{76^3+25^3}{101}-76\cdot 25=\dfrac{(76+25)(76^2-76\cdot 25+25^2)}{101}-76\cdot 25=\\\\\\=\dfrac{101\cdot (76^2-76\cdot 25+25^2)}{101}-76\cdot 25= (76^2-76\cdot 25+25^2)-76\cdot 25=\\\\\\=76^2-2\cdot 76\cdot 25+25^2=(76-25)^2=51^2=2601$

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