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受欢迎的代数 >

(x-3)^4-8(x-3)^2-9=0

解答

(x - 3)^{4} - 8 (x - 3)^{2} - 9 = 0

解答

x = 0, x = 6, x = 3 + i, x = 3 - i

求解步骤

(x - 3)^{4} - 8 (x - 3)^{2} - 9 = 0

展开

(x - 3)^{4} - 8 (x - 3)^{2} - 9 : x^{4} - 12 x^{3} + 46 x^{2} - 60 x

x^{4} - 12 x^{3} + 46 x^{2} - 60 x = 0

因式分解

x^{4} - 12 x^{3} + 46 x^{2} - 60 x : x (x - 6) (x^{2} - 6 x + 10)

x (x - 6) (x^{2} - 6 x + 10) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x = 0 or x - 6 = 0 or x^{2} - 6 x + 10 = 0

解

x - 6 = 0 : x = 6

解

x^{2} - 6 x + 10 = 0 : x = 3 + i, x = 3 - i

解为

x = 0, x = 6, x = 3 + i, x = 3 - i

作图

流行的例子

x^{9} + x^{6} = 36

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

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

根 x^3-6x^2+11x-6

roo t s x^{3} - 6 x^{2} + 11 x - 6