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受欢迎的代数 >

x^4-6x^3+10x^2-6x+1=0

解答

x^{4} - 6 x^{3} + 10 x^{2} - 6 x + 1 = 0

解答

x = 1, x = 2 + 3, x = 2 - 3

+1

十进制

x = 1, x = 3.73205 \dots, x = 0.26794 \dots

求解步骤

x^{4} - 6 x^{3} + 10 x^{2} - 6 x + 1 = 0

因式分解

x^{4} - 6 x^{3} + 10 x^{2} - 6 x + 1 : (x - 1)^{2} (x^{2} - 4 x + 1)

(x - 1)^{2} (x^{2} - 4 x + 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x - 1 = 0 or x^{2} - 4 x + 1 = 0

解

x - 1 = 0 : x = 1

解

x^{2} - 4 x + 1 = 0 : x = 2 + 3, x = 2 - 3

解为

x = 1, x = 2 + 3, x = 2 - 3

作图

流行的例子

0=4x^3-48x^2+84x-39.6

0 = 4 x^{3} - 48 x^{2} + 84 x - 39.6

(1-y)(3-y)(6-y)=120

(1 - y) (3 - y) (6 - y) = 120

solvefor x,x^3+y=5

so l v e f or x, x^{3} + y = 5

x^3-x^2-x*2^1=0

x^{3} - x^{2} - x \cdot 2^{1} = 0

solvefor t,(t^4-1)^2=x

so l v e f or t, (t^{4} - 1)^{2} = x