Найдите значение выражения (а-3)^2+(а+2)^2-2(3-а)(а+2), если а=1/3. Created by stoyanovspoztvmy. algebra-ru

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daraprelj

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(а-3)²+(а+2)²-2*(3-а)(а+2), если а=1/3

(а-3)²+(а+2)²-2*(3-а)(а+2) = a²-6a+9+a²+4a+4-2*(3a+6-a²-2a) = 2a²-2a+13+2a²-2a-12 = 4a²-4a+1 = (2a-1)²

(2a-1)²,если а=1/3

(2*1/3-1)²=(2/3-1)²=(-1/3)²=1/9

Ответ: 1/9

4 votes Thanks 6

L0sK

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Ответ:

$\frac{1}{9}$

Объяснение:

(a-3)²+(a+2)²-2(3-a)(a+2) = (a-3)² + (a+2)(a+2) - 2(3-a)) = (a-3)² + (a+2)(a + 2 - 6 + 2a) = (a-3)² + (a+2)(3a-4) = (a-3)² + (3a² - 4a + 6a -8) = (a-3)² + (3a² - 2a - 8) = a² - 6a + 9 + 3a² - 2a - 8 = 4a² - 8a + 1 = (2a - 1)²

Если а = $\frac{1}{3}$ , получим:

$(\frac{2}{3} - 1)^2 = (-\frac{1}{3})^2 = \frac{1}{9}$

2 votes Thanks 3

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