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受欢迎的代数 >

(x+6)(x+1)(x+3)(x-2)+56=0

解答

(x + 6) (x + 1) (x + 3) (x - 2) + 56 = 0

解答

x = 1, x = - 5, x = 2 (2 - 1), x = - 2 (1 + 2)

+1

十进制

x = 1, x = - 5, x = 0.82842 \dots, x = - 4.82842 \dots

求解步骤

(x + 6) (x + 1) (x + 3) (x - 2) + 56 = 0

展开

(x + 6) (x + 1) (x + 3) (x - 2) + 56 : x^{4} + 8 x^{3} + 7 x^{2} - 36 x + 20

x^{4} + 8 x^{3} + 7 x^{2} - 36 x + 20 = 0

因式分解

x^{4} + 8 x^{3} + 7 x^{2} - 36 x + 20 : (x - 1) (x + 5) (x^{2} + 4 x - 4)

(x - 1) (x + 5) (x^{2} + 4 x - 4) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x - 1 = 0 or x + 5 = 0 or x^{2} + 4 x - 4 = 0

解

x - 1 = 0 : x = 1

解

x + 5 = 0 : x = - 5

解

x^{2} + 4 x - 4 = 0 : x = 2 (2 - 1), x = - 2 (1 + 2)

解为

x = 1, x = - 5, x = 2 (2 - 1), x = - 2 (1 + 2)

作图

流行的例子

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

x^{3} + x = 100

130r^3-a^2r^3+a^2=0

130 r^{3} - a^{2} r^{3} + a^{2} = 0

x^{5} = 212

2 x^{3} + 2 x + x = - 1