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受欢迎的代数 >

ax^4+bx^2+c=0

解答

a x^{4} + b x^{2} + c = 0

解答

x = \frac{- b + b ^{2} - 4 a c}{2 a}, x = - \frac{- b + b ^{2} - 4 a c}{2 a}, x = \frac{- b - b ^{2} - 4 a c}{2 a}, x = - \frac{- b - b ^{2} - 4 a c}{2 a}

求解步骤

a x^{4} + b x^{2} + c = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

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

解

a u^{2} + b u + c = 0 : u = \frac{- b + b ^{2} - 4 a c}{2 a}, u = \frac{- b - b ^{2} - 4 a c}{2 a}; a \neq = 0

u = \frac{- b + b ^{2} - 4 a c}{2 a}, u = \frac{- b - b ^{2} - 4 a c}{2 a}; a \neq = 0

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{- b + b ^{2} - 4 a c}{2 a} : x = \frac{- b + b ^{2} - 4 a c}{2 a}, x = - \frac{- b + b ^{2} - 4 a c}{2 a}

解

x^{2} = \frac{- b - b ^{2} - 4 a c}{2 a} : x = \frac{- b - b ^{2} - 4 a c}{2 a}, x = - \frac{- b - b ^{2} - 4 a c}{2 a}

解为

x = \frac{- b + b ^{2} - 4 a c}{2 a}, x = - \frac{- b + b ^{2} - 4 a c}{2 a}, x = \frac{- b - b ^{2} - 4 a c}{2 a}, x = - \frac{- b - b ^{2} - 4 a c}{2 a}

作图

流行的例子

x^5+5x^4-2x^3-10x^2+x+5=0

x^{5} + 5 x^{4} - 2 x^{3} - 10 x^{2} + x + 5 = 0

(x-3)^4+(x-5)^4=20

(x - 3)^{4} + (x - 5)^{4} = 20

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10x^9-9x^{10}=0.75

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