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受欢迎的代数 >

(2x+1)^2-(x^2+2)(x^2-2)=4,x+1/4-3=4

解答

(2 x + 1)^{2} - (x^{2} + 2) (x^{2} - 2) = 4, x + \frac{1}{4} - 3 = 4

解答

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

+1

十进制

x = - 1, x = 2.41421 \dots, x = - 0.41421 \dots

求解步骤

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

展开

(2 x + 1)^{2} - (x^{2} + 2) (x^{2} - 2) : - x^{4} + 4 x^{2} + 4 x + 5

- x^{4} + 4 x^{2} + 4 x + 5 = 4

将

4

para o lado esquerdo

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

因式分解

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

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

解

x + 1 = 0 : x = - 1

解

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

解为

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

作图

流行的例子

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8 x^{4} - 96 x^{3} + 320 x^{2} + 588 x - 1764 = 0

m^{4} = 625

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