Предмет: Алгебра, автор: marishka8212

доказать что значение выражения (а+в)(а+в)-2(а+в-1) при любых а и в является неотрицательным

Ответы

Автор ответа: manyny06

0

(а+в)² - 2(а+в) +2 = (а+в)²- 2* (а+в) + 1 + 1 = (а+в-1)² + 1
(а+в-1) больше нуля, т.к. в четной степени
1 - положительное число,
а сумма двух положительных чисел (выражений) всегда является неотрицательным, что и требовалось доказать

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