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受欢迎的代数 >

1000=x(30-2x)(20-2x)

解答

1000 = x (30 - 2 x) (20 - 2 x)

解答

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

+1

十进制

x = 5, x = 17.07106 \dots, x = 2.92893 \dots

求解步骤

1000 = x (30 - 2 x) (20 - 2 x)

展开

x (30 - 2 x) (20 - 2 x) : 600 x - 100 x^{2} + 4 x^{3}

1000 = 600 x - 100 x^{2} + 4 x^{3}

交换两边

600 x - 100 x^{2} + 4 x^{3} = 1000

将

1000

para o lado esquerdo

600 x - 100 x^{2} + 4 x^{3} - 1000 = 0

改写成标准形式

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

4 x^{3} - 100 x^{2} + 600 x - 1000 = 0

因式分解

4 x^{3} - 100 x^{2} + 600 x - 1000 : 4 (x - 5) (x^{2} - 20 x + 50)

4 (x - 5) (x^{2} - 20 x + 50) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

x - 5 = 0 or x^{2} - 20 x + 50 = 0

解

x - 5 = 0 : x = 5

解

x^{2} - 20 x + 50 = 0 : x = 5 (2 + 2), x = 5 (2 - 2)

解为

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

作图

流行的例子

(x-1)^4+5(x-1)^2+9=0

(x - 1)^{4} + 5 (x - 1)^{2} + 9 = 0

solvefor x,y^2=x^3+7

so l v e f or x, y^{2} = x^{3} + 7

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

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

x^3+4x^2-25x-100=0

x^{3} + 4 x^{2} - 25 x - 100 = 0

-x^3-10x^2-33x-36=0

- x^{3} - 10 x^{2} - 33 x - 36 = 0