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受欢迎的代数 >

(1-r)^3=3-3r

解答

(1 - r)^{3} = 3 - 3 r

解答

r = 1, r = 1 + 3, r = 1 - 3

+1

十进制

r = 1, r = 2.73205 \dots, r = - 0.73205 \dots

求解步骤

(1 - r)^{3} = 3 - 3 r

展开

(1 - r)^{3} : 1 - 3 r + 3 r^{2} - r^{3}

1 - 3 r + 3 r^{2} - r^{3} = 3 - 3 r

将

3 r

para o lado esquerdo

- r^{3} + 3 r^{2} + 1 = 3

将

3

para o lado esquerdo

- r^{3} + 3 r^{2} - 2 = 0

因式分解

- r^{3} + 3 r^{2} - 2 : - (r - 1) (r^{2} - 2 r - 2)

- (r - 1) (r^{2} - 2 r - 2) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

r - 1 = 0 or r^{2} - 2 r - 2 = 0

解

r - 1 = 0 : r = 1

解

r^{2} - 2 r - 2 = 0 : r = 1 + 3, r = 1 - 3

解为

r = 1, r = 1 + 3, r = 1 - 3

作图

流行的例子

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x^{3} - 5 x^{2} + 4 x + 10 = 0

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log_{2}(256)=(x^3)/8

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