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Alena7Danilova
@Alena7Danilova
July 2022
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Известно, что a^2+b^2+c^2=21, a+b-c=7. Найдите значение выражения ab-bc-ac. Помогите, буду очень благодарна
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magicmasha
(a+b-c)(a+b-c)=49;
a^2+ab-ac+ab+b^2-bc-ac-bc+c^2=49;
(a^2+b^2+c^2)+2ab-2ac-2bc=49;
21+2(ab-ac-bc)=49;
2(ab-ac-bc)=49-21;
ab-bc-ac=28/2=14.
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Answers & Comments
a^2+ab-ac+ab+b^2-bc-ac-bc+c^2=49;
(a^2+b^2+c^2)+2ab-2ac-2bc=49;
21+2(ab-ac-bc)=49;
2(ab-ac-bc)=49-21;
ab-bc-ac=28/2=14.