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受欢迎的代数 >

192pi=2pix16+2pi*x^2

解答

192 π = 2 π \cdot x \cdot 16 + 2 π \cdot x^{2}

解答

x = 4 (10 - 2), x = - 4 (2 + 10)

+1

十进制

x = 4.64911 \dots, x = - 20.64911 \dots

求解步骤

192 π = 2 π x \cdot 16 + 2 π x^{2}

展开

2 π x \cdot 16 + 2 π x^{2} : 32 π x + 2 π x^{2}

192 π = 32 π x + 2 π x^{2}

交换两边

32 π x + 2 π x^{2} = 192 π

将

192 π

para o lado esquerdo

32 π x + 2 π x^{2} - 192 π = 0

改写成标准形式

a x^{2} + b x + c = 0

2 π x^{2} + 32 π x - 192 π = 0

使用求根公式求解

x_{1, 2} = \frac{- 32 π \pm ( 32 π ) ^{2} - 4 \cdot 2 π ( - 192 π )}{2 \cdot 2 π}

(32 π)^{2} - 4 \cdot 2 π (- 192 π) = 1610 π

x_{1, 2} = \frac{- 32 π \pm 16 10 π}{2 \cdot 2 π}

将解分隔开

x_{1} = \frac{- 32 π + 16 10 π}{2 \cdot 2 π}, x_{2} = \frac{- 32 π - 16 10 π}{2 \cdot 2 π}

x = \frac{- 32 π + 16 10 π}{2 \cdot 2 π} : 4 (10 - 2)

x = \frac{- 32 π - 16 10 π}{2 \cdot 2 π} : - 4 (2 + 10)

二次方程组的解是:

x = 4 (10 - 2), x = - 4 (2 + 10)

作图

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