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受欢迎的代数 >

(x^2-6x)^2+2*(x-3)^2=81

解答

(x^{2} - 6 x)^{2} + 2 \cdot (x - 3)^{2} = 81

解答

x = - 1, x = 3, x = 7

求解步骤

(x^{2} - 6 x)^{2} + 2 (x - 3)^{2} = 81

展开

(x^{2} - 6 x)^{2} + 2 (x - 3)^{2} : x^{4} - 12 x^{3} + 38 x^{2} - 12 x + 18

x^{4} - 12 x^{3} + 38 x^{2} - 12 x + 18 = 81

将

81

para o lado esquerdo

x^{4} - 12 x^{3} + 38 x^{2} - 12 x - 63 = 0

因式分解

x^{4} - 12 x^{3} + 38 x^{2} - 12 x - 63 : (x + 1) (x - 3)^{2} (x - 7)

(x + 1) (x - 3)^{2} (x - 7) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x + 1 = 0 or x - 3 = 0 or x - 7 = 0

解

x + 1 = 0 : x = - 1

解

x - 3 = 0 : x = 3

解

x - 7 = 0 : x = 7

解为

x = - 1, x = 3, x = 7

作图

流行的例子

6 x^{7} - 8 = 2 (7 - 10)

(x^2-8)^2+x^2-8=20

(x^{2} - 8)^{2} + x^{2} - 8 = 20

x^3+7x^2+17x-24=0

x^{3} + 7 x^{2} + 17 x - 24 = 0

(x^2-1)(x^2-12)+24=0

(x^{2} - 1) (x^{2} - 12) + 24 = 0

-(12x^5-8x^3)=25x^2

- (12 x^{5} - 8 x^{3}) = 25 x^{2}