Question

вычислите рациональным способом
71^3+49^3
________ -71*49
120

Answer 1

$\frac{71^{3}+49^{3}}{120}-71*49=\frac{(71+49)(71^{2}-71*49+49^{2})}{120}-71*49=\frac{120(71^{2}-71*49+49^{2})}{120}-71*49=71^{2}-71*49+49^{2}-71*49=71^{2}-2*71*49+49^{2}=(71-49)^{2} =22^{2}=484$