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受欢迎的代数 >

solvefor y,40x^2+3y^2-7x+y+1=0

解答

求解

y, 40 x^{2} + 3 y^{2} - 7 x + y + 1 = 0

解答

y = \frac{- 1 + - 480 x ^{2} + 84 x - 11}{6}, y = \frac{- 1 - - 480 x ^{2} + 84 x - 11}{6}

求解步骤

40 x^{2} + 3 y^{2} - 7 x + y + 1 = 0

改写成标准形式

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

3 y^{2} + y + 40 x^{2} - 7 x + 1 = 0

使用求根公式求解

y_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 3 ( 40 x ^{2} - 7 x + 1 )}{2 \cdot 3}

化简

1^{2} - 4 \cdot 3 (40 x^{2} - 7 x + 1) : - 480 x^{2} + 84 x - 11

y_{1, 2} = \frac{- 1 \pm - 480 x ^{2} + 84 x - 11}{2 \cdot 3}

将解分隔开

y_{1} = \frac{- 1 + - 480 x ^{2} + 84 x - 11}{2 \cdot 3}, y_{2} = \frac{- 1 - - 480 x ^{2} + 84 x - 11}{2 \cdot 3}

y = \frac{- 1 + - 480 x ^{2} + 84 x - 11}{2 \cdot 3} : \frac{- 1 + - 480 x ^{2} + 84 x - 11}{6}

y = \frac{- 1 - - 480 x ^{2} + 84 x - 11}{2 \cdot 3} : \frac{- 1 - - 480 x ^{2} + 84 x - 11}{6}

二次方程组的解是:

y = \frac{- 1 + - 480 x ^{2} + 84 x - 11}{6}, y = \frac{- 1 - - 480 x ^{2} + 84 x - 11}{6}

作图

流行的例子

t^{2} + 6 t - 4 = 0

x^{2} + 6 x + 19 = 4 x

10x^2-39/2 x+9=0

10 x^{2} - \frac{39}{2} x + 9 = 0

x^{2} + 20 x - 4 = 0

3(3x+5)^2-36=-21

3 (3 x + 5)^{2} - 36 = - 21