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受欢迎的代数 >

9x^4=25x^2-16

解答

9 x^{4} = 25 x^{2} - 16

解答

x = \frac{4}{3}, x = - \frac{4}{3}, x = 1, x = - 1

+1

十进制

x = 1.33333 \dots, x = - 1.33333 \dots, x = 1, x = - 1

求解步骤

9 x^{4} = 25 x^{2} - 16

将

16

para o lado esquerdo

9 x^{4} + 16 = 25 x^{2}

将

25 x^{2}

para o lado esquerdo

9 x^{4} + 16 - 25 x^{2} = 0

改写成标准形式

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

9 x^{4} - 25 x^{2} + 16 = 0

用

u = x^{2}

和

u^{2} = x^{4}

改写方程式

9 u^{2} - 25 u + 16 = 0

解

9 u^{2} - 25 u + 16 = 0 : u = \frac{16}{9}, u = 1

u = \frac{16}{9}, u = 1

代回

u = x^{2}

，求解

x

解

x^{2} = \frac{16}{9} : x = \frac{4}{3}, x = - \frac{4}{3}

解

x^{2} = 1 : x = 1, x = - 1

解为

x = \frac{4}{3}, x = - \frac{4}{3}, x = 1, x = - 1

作图

流行的例子

solvefor x,x^3+y^3-z^3=4

so l v e f or x, x^{3} + y^{3} - z^{3} = 4

x^3-2x-5=0,(x=2.0813)

x^{3} - 2 x - 5 = 0, (x = 2.0813)

(x-1/3)(x^2+x(0.1)/3+(1^2)/(3^2))=64

(x - \frac{1}{3}) (x^{2} + x \frac{0.1}{3} + \frac{1 ^{2}}{3 ^{2}}) = 64

(x-7)^4=(x-7)^5

(x - 7)^{4} = (x - 7)^{5}

x^{3} = - 125