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受欢迎的代数 >

3(4g^6)=2(6g^9)

解答

3 (4 g^{6}) = 2 (6 g^{9})

解答

g = 0, g = 1, g = - \frac{1}{2} + i \frac{3}{2}, g = - \frac{1}{2} - i \frac{3}{2}

求解步骤

3 (4 g^{6}) = 2 (6 g^{9})

将

2 (6 g^{9})

para o lado esquerdo

3 \cdot 4 g^{6} - 2 \cdot 6 g^{9} = 0

因式分解

3 \cdot 4 g^{6} - 2 \cdot 6 g^{9} : - 12 g^{6} (g - 1) (g^{2} + g + 1)

- 12 g^{6} (g - 1) (g^{2} + g + 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

g = 0 or g - 1 = 0 or g^{2} + g + 1 = 0

解

g - 1 = 0 : g = 1

解

g^{2} + g + 1 = 0 : g = - \frac{1}{2} + i \frac{3}{2}, g = - \frac{1}{2} - i \frac{3}{2}

解为

g = 0, g = 1, g = - \frac{1}{2} + i \frac{3}{2}, g = - \frac{1}{2} - i \frac{3}{2}

作图

流行的例子

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

x^{11}+2/9 x=32

x^{11} + \frac{2}{9} x = 32

x^4+32x^2+256=0

x^{4} + 32 x^{2} + 256 = 0

2 x^{3} + 28 = 4

x^{3} + 7 x^{2} = - 10 x