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受欢迎的代数 >

(6-x)^4+(8-x)^4=16

解答

(6 - x)^{4} + (8 - x)^{4} = 16

解答

x = 6, x = 8, x = 7 + 7 i, x = 7 - 7 i

求解步骤

(6 - x)^{4} + (8 - x)^{4} = 16

展开

(6 - x)^{4} + (8 - x)^{4} : 2 x^{4} - 56 x^{3} + 600 x^{2} - 2912 x + 5392

2 x^{4} - 56 x^{3} + 600 x^{2} - 2912 x + 5392 = 16

将

16

para o lado esquerdo

2 x^{4} - 56 x^{3} + 600 x^{2} - 2912 x + 5376 = 0

因式分解

2 x^{4} - 56 x^{3} + 600 x^{2} - 2912 x + 5376 : 2 (x - 6) (x - 8) (x^{2} - 14 x + 56)

2 (x - 6) (x - 8) (x^{2} - 14 x + 56) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x - 6 = 0 or x - 8 = 0 or x^{2} - 14 x + 56 = 0

解

x - 6 = 0 : x = 6

解

x - 8 = 0 : x = 8

解

x^{2} - 14 x + 56 = 0 : x = 7 + 7 i, x = 7 - 7 i

解为

x = 6, x = 8, x = 7 + 7 i, x = 7 - 7 i

作图

流行的例子

x^{5} - 1 = 0

x^{4} - 8 x^{2} = - 16

x^3-6x^3+3x+10=0

x^{3} - 6 x^{3} + 3 x + 10 = 0

x^3+2x^2-9x-18=0

x^{3} + 2 x^{2} - 9 x - 18 = 0

x^{4} + 4 x^{2} + 16 = 0