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受欢迎的代数 >

solvefor x,g(1-t)=3x^2-5x+1

解答

求解

x, g (1 - t) = 3 x^{2} - 5 x + 1

解答

x = \frac{5 + 12 g - 12 t g + 13}{6}, x = \frac{5 - 12 g - 12 t g + 13}{6}

求解步骤

g (1 - t) = 3 x^{2} - 5 x + 1

展开

g (1 - t) : g - t g

g - t g = 3 x^{2} - 5 x + 1

交换两边

3 x^{2} - 5 x + 1 = g - t g

将

t g

para o lado esquerdo

3 x^{2} - 5 x + 1 + t g = g

将

g

para o lado esquerdo

3 x^{2} - 5 x + 1 + t g - g = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 3 ( 1 + t g - g )}{2 \cdot 3}

化简

(- 5)^{2} - 4 \cdot 3 (1 + t g - g) : 12 g - 12 t g + 13

x_{1, 2} = \frac{- ( - 5 ) \pm 12 g - 12 t g + 13}{2 \cdot 3}

将解分隔开

x_{1} = \frac{- ( - 5 ) + 12 g - 12 t g + 13}{2 \cdot 3}, x_{2} = \frac{- ( - 5 ) - 12 g - 12 t g + 13}{2 \cdot 3}

x = \frac{- ( - 5 ) + 12 g - 12 t g + 13}{2 \cdot 3} : \frac{5 + 12 g - 12 t g + 13}{6}

x = \frac{- ( - 5 ) - 12 g - 12 t g + 13}{2 \cdot 3} : \frac{5 - 12 g - 12 t g + 13}{6}

二次方程组的解是:

x = \frac{5 + 12 g - 12 t g + 13}{6}, x = \frac{5 - 12 g - 12 t g + 13}{6}

作图

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