←Vrati se na zadatke1. ZadatakIzračunaj: 143⋅91⋅77−143⋅91⋅77.143\cdot91\cdot77-\sqrt{143}\cdot\sqrt{91}\cdot\sqrt{77}.143⋅91⋅77−143⋅91⋅77.Rješenje143⋅91⋅77−143⋅91⋅77=11⋅13⋅7⋅13⋅7⋅11−11⋅13⋅7⋅13⋅7⋅11=(11⋅13⋅7)2−(11⋅13⋅7)2=10012−(1001)2=10012−1001=1001⋅(1001−1)=1001⋅1000=1001000.\begin{aligned} 143\cdot91\cdot77-\sqrt{143}\cdot\sqrt{91}\cdot\sqrt{77} &=11\cdot13\cdot7\cdot13\cdot7\cdot11 -\sqrt{11}\cdot\sqrt{13}\cdot\sqrt7\cdot\sqrt{13}\cdot\sqrt7\cdot\sqrt{11}\\ &=(11\cdot13\cdot7)^2-(\sqrt{11}\cdot\sqrt{13}\cdot\sqrt7)^2\\ &=1001^2-(\sqrt{1001})^2\\ &=1001^2-1001\\ &=1001\cdot(1001-1)\\ &=1001\cdot1000\\ &=1001000. \end{aligned}143⋅91⋅77−143⋅91⋅77=11⋅13⋅7⋅13⋅7⋅11−11⋅13⋅7⋅13⋅7⋅11=(11⋅13⋅7)2−(11⋅13⋅7)2=10012−(1001)2=10012−1001=1001⋅(1001−1)=1001⋅1000=1001000.
