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人気のある代数 >

solvefor x,f(x)^4+f(-x)^4=x^{2000}

解

解く

x, f (x)^{4} + f (- x)^{4} = x^{2000}

解

x = 0, x = 4992 499 f, x = - 4992 499 f, x = 4 4992 499 f, x = - 4 4992 499 f

解答ステップ

f x^{4} + f (- x)^{4} = x^{2000}

拡張

f x^{4} + f (- x)^{4} : 2 x^{4} f

2 x^{4} f = x^{2000}

辺を交換する

x^{2000} = 2 x^{4} f

2 x^{4} f

を左側に移動します

x^{2000} - 2 x^{4} f = 0

標準的な形式で書く

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

x^{2000} - 2 f x^{4} = 0

equationを

u = x^{2}, u^{2} = x^{4}

と以下で書き換える:

u^{1000} = x^{2000}

u^{1000} - 2 f u^{2} = 0

解く

u^{1000} - 2 f u^{2} = 0 : u = 0, u = 4992 499 f, u = - 4992 499 f

u = 0, u = 4992 499 f, u = - 4992 499 f

再び

u = x^{2}

に置き換えて以下を解く:

x

解く

x^{2} = 0 : x = 0

解く

x^{2} = 4992 499 f : x = 4992 499 f, x = - 4992 499 f

解く

x^{2} = - 4992 499 f : x = 4 4992 499 f, x = - 4 4992 499 f

解答は

x = 0, x = 4992 499 f, x = - 4992 499 f, x = 4 4992 499 f, x = - 4 4992 499 f

グラフ

人気の例

2a^3-3a^2+2a+1=0

2 a^{3} - 3 a^{2} + 2 a + 1 = 0

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

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

1 x^{3} - 7 x + 6 = 0

-8x-12+x^3+x^2=0

- 8 x - 12 + x^{3} + x^{2} = 0

0 = x^{3} - x + 1