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受欢迎的代数 >

solvefor x,f=[n]x3+[m]x^2-[p]x+[q]

解答

求解

x, f = [n] x 3 + [m] x^{2} - [p] x + [q]

解答

x = \frac{- 3 n + p + ( 3 n - p ) ^{2} - 4 m ( q - f )}{2 m}, x = \frac{- 3 n + p - ( 3 n - p ) ^{2} - 4 m ( q - f )}{2 m}; m \neq = 0

求解步骤

f = [n] x \cdot 3 + [m] x^{2} - [p] x + [q]

展开

(n) x \cdot 3 + (m) x^{2} - (p) x + (q) : 3 n x + m x^{2} - p x + q

f = 3 n x + m x^{2} - p x + q

交换两边

3 n x + m x^{2} - p x + q = f

将

f

para o lado esquerdo

3 n x + m x^{2} - p x + q - f = 0

改写成标准形式

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

m x^{2} + (3 n - p) x + q - f = 0

使用求根公式求解

x_{1, 2} = \frac{- ( 3 n - p ) \pm ( 3 n - p ) ^{2} - 4 m ( q - f )}{2 m}

x = \frac{- ( 3 n - p ) + ( 3 n - p ) ^{2} - 4 m ( q - f )}{2 m} : \frac{- 3 n + p + ( 3 n - p ) ^{2} - 4 m ( q - f )}{2 m}

x = \frac{- ( 3 n - p ) - ( 3 n - p ) ^{2} - 4 m ( q - f )}{2 m} : \frac{- 3 n + p - ( 3 n - p ) ^{2} - 4 m ( q - f )}{2 m}

二次方程组的解是:

x = \frac{- 3 n + p + ( 3 n - p ) ^{2} - 4 m ( q - f )}{2 m}, x = \frac{- 3 n + p - ( 3 n - p ) ^{2} - 4 m ( q - f )}{2 m}; m \neq = 0

作图

流行的例子

v^{2} - 2 v = 3

a^{2} - 9 a + 2 = 0

solvefor x,p(x)=y(x^2+2)-x(y^2+2)

so l v e f or x, p (x) = y (x^{2} + 2) - x (y^{2} + 2)

- X^{2} - 2 X + 1 = 0

solvefor x,f^{-1}(x)=2-(x-3)^2

so l v e f or x, f^{- 1} (x) = 2 - (x - 3)^{2}