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受欢迎的代数 >

x^2+6x+9=4x^4

解答

x^{2} + 6 x + 9 = 4 x^{4}

解答

x = - \frac{1}{4} + i \frac{23}{4}, x = - \frac{1}{4} - i \frac{23}{4}, x = - 1, x = \frac{3}{2}

求解步骤

x^{2} + 6 x + 9 = 4 x^{4}

交换两边

4 x^{4} = x^{2} + 6 x + 9

将

9

para o lado esquerdo

4 x^{4} - 9 = x^{2} + 6 x

将

6 x

para o lado esquerdo

4 x^{4} - 9 - 6 x = x^{2}

将

x^{2}

para o lado esquerdo

4 x^{4} - 9 - 6 x - x^{2} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

4 x^{4} - x^{2} - 6 x - 9 = 0

因式分解

4 x^{4} - x^{2} - 6 x - 9 : (2 x^{2} + x + 3) (x + 1) (2 x - 3)

(2 x^{2} + x + 3) (x + 1) (2 x - 3) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

2 x^{2} + x + 3 = 0 or x + 1 = 0 or 2 x - 3 = 0

解

2 x^{2} + x + 3 = 0 : x = - \frac{1}{4} + i \frac{23}{4}, x = - \frac{1}{4} - i \frac{23}{4}

解

x + 1 = 0 : x = - 1

解

2 x - 3 = 0 : x = \frac{3}{2}

解为

x = - \frac{1}{4} + i \frac{23}{4}, x = - \frac{1}{4} - i \frac{23}{4}, x = - 1, x = \frac{3}{2}

作图

流行的例子

1400=700(1+x/(100))^5

1400 = 700 (1 + \frac{x}{100})^{5}

(xx^8)/5 =(-2)/(25)

\frac{x x ^{8}}{5} = \frac{- 2}{25}

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

x^{4} - 7 x = 0

- 10 = 4 x^{4} - 10