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受欢迎的三角函数 >

3cos^2(x)+2cos(x)-8=0

解答

3 cos^{2} (x) + 2 cos (x) - 8 = 0

解答

x \in R 无解

求解步骤

3 cos^{2} (x) + 2 cos (x) - 8 = 0

用替代法求解

3 cos^{2} (x) + 2 cos (x) - 8 = 0

令

: cos (x) = u

3 u^{2} + 2 u - 8 = 0

3 u^{2} + 2 u - 8 = 0 : u = \frac{4}{3}, u = - 2

3 u^{2} + 2 u - 8 = 0

使用求根公式求解

3 u^{2} + 2 u - 8 = 0

二次方程求根公式:

若

a = 3, b = 2, c = - 8

u_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 3 ( - 8 )}{2 \cdot 3}

u_{1, 2} = \frac{- 2 \pm 2 ^{2} - 4 \cdot 3 ( - 8 )}{2 \cdot 3}

2^{2} - 4 \cdot 3 (- 8) = 10

2^{2} - 4 \cdot 3 (- 8)

使用法则

- (- a) = a

= 2^{2} + 4 \cdot 3 \cdot 8

数字相乘:

4 \cdot 3 \cdot 8 = 96

= 2^{2} + 96

2^{2} = 4

= 4 + 96

数字相加:

4 + 96 = 100

= 100

因式分解数字:

100 = 1 0^{2}

= 1 0^{2}

使用根式运算法则:

n a^{n} = a

1 0^{2} = 10

= 10

u_{1, 2} = \frac{- 2 \pm 10}{2 \cdot 3}

将解分隔开

u_{1} = \frac{- 2 + 10}{2 \cdot 3}, u_{2} = \frac{- 2 - 10}{2 \cdot 3}

u = \frac{- 2 + 10}{2 \cdot 3} : \frac{4}{3}

\frac{- 2 + 10}{2 \cdot 3}

数字相加/相减:

- 2 + 10 = 8

= \frac{8}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{8}{6}

约分:

2

= \frac{4}{3}

u = \frac{- 2 - 10}{2 \cdot 3} : - 2

\frac{- 2 - 10}{2 \cdot 3}

数字相减:

- 2 - 10 = - 12

= \frac{- 12}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{- 12}{6}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{12}{6}

数字相除:

\frac{12}{6} = 2

= - 2

二次方程组的解是:

u = \frac{4}{3}, u = - 2

u = cos (x)

代回

cos (x) = \frac{4}{3}, cos (x) = - 2

cos (x) = \frac{4}{3}, cos (x) = - 2

cos (x) = \frac{4}{3} :

无解

cos (x) = \frac{4}{3}

- 1 \leq cos (x) \leq 1

无解

cos (x) = - 2 :

无解

cos (x) = - 2

- 1 \leq cos (x) \leq 1

无解

合并所有解

x \in R 无解

作图

流行的例子

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tan (a) + sec (a) = \frac{3}{2}

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