求解方程 (2x – 3) ^2/3 = 4

代数是数学的一个分支，它包括带有运算符的数字和变量。具有恒定值的项称为数字，它由数字表示。没有常数值的项称为变量，它的值不固定，用字母和符号表示。代数基本上用于计算未知数的值。借助问题中给出的信息，我们应用该操作并获得未知数的值。

代数表达式

代数表达式是在数字、变量和适当的运算符的帮助下将数学语句表示为数学形式。

例如：“一个数加到 12 的三次”可以写为“3x + 12”。这里我们不知道数字的值，所以我们假设它为 x，它可以取任何值。加号将语句分成两部分，我们将其命名为术语。在 3x + 12 中，有两项。

因此，根据项的数量，代数表达式可以分为以下几种类型。

• 单项式：如果表达式中的项数为一个，则称为单项式。示例：5x、6y 等
• 二项式：如果表达式中的项数为两个，则称为二项式。例如：5x+3、12y-3 等。
• 三项式：如果表达式中的项数为三，则称为三项式表达式。例如：5x-6y+3z、5q-6f+3x等。
• 多项式：如果表达式中的项数为一项或多项，则称为多项式。

方程的解：

Earlier in this article, we said, variables can take any value. But when we compare an algebraic expression with numerals then these variables should have any fixed value. With the help mathematical operation, we can find the value of the variables. The solution of an equation is the value of numerals at which the given equation got satisfied. The left-hand side and right-hand side of the equation should have to equal.

求解方程 (2x – 3) ^2/3 = 4

解决方案：

Step to solve the problem:

Step 1: To solve the exponent of an equation, do the inverse operation on both sides.

In the given problem, we can clearly see there is the cube root and square on the variable part so the inverse operation is the cube and square root respectively.

⇒ (2x – 3) = 4^(3/2)

⇒ (2x – 3) = (4³)^(1/2)

⇒ (2x – 3) = (64)^(1/2)

As we know that the square root of 64 is +8 and -8.

Step 2: Here we have two cases because the square root of 64 gives two values.

Case 1: When the square root is +8

⇒ 2x – 3 = 8

Case 2: When the square root is -8.

⇒ 2x – 3 = -8

Step 3: Transfer all the numerals on one side and all the variables on the other side of the equal sign. And get the value of the variables.

Case 1:                                                        

⇒ 2x – 3 = 8

⇒ 2x = 8 + 3

⇒ 2x = 11

⇒ x = 11/2

Case 2: 

⇒ 2x – 3 = -8

⇒ 2x = -8 + 3 

⇒ 2x = -5

⇒ x = -5/2

So the solutions of the given equation are x = 11/2 and x = -5/2.

类似问题

问题 1：找出方程的所有解：(x – 2) ^2/3 = 9。

解决方案：

In the given problem, we can clearly see there is the cube root and square on the variable part so the inverse operation is the cube and square root respectively.

⇒ (x – 2) = 9^(3/2)

⇒ (x – 2) = (9³)^(1/2)

⇒ (x – 2) = (729)^(1/2)

So, the square root of 729 is -27 and +27. So we have two cases.

Case 1:

⇒ (x – 2) = 27

⇒ x = 27 + 2

⇒ x = 29

Case 2: 

⇒ (x – 2) = -27

⇒ x = -27 + 2

⇒ x = -25

So the solution of the given equation is x = +29 and x = -25.

问题 2：找出方程的所有解：(3x – 2) ^2/3 = 1。

解决方案：

In the given problem, we can clearly see there is the cube root and square on the variable part so the inverse operation is the cube and square root respectively.

⇒ (3x – 2) = 1^(3/2)

⇒ (3x – 2) = (1³)^(1/2)

⇒ (3x – 2) = 1^(1/2)

So, the square root of 1 is +1 and -1. So we have two cases.

Case 1:

⇒ 3x – 2 = 1

⇒ 3x = 1 + 2

⇒ 3x = 3

⇒ x = 1

Case 2: 

⇒ 3x – 2 = -1

⇒ 3x = -1 + 2

⇒ 3x = +1

⇒ x = 1/3

So the solution of the given question is  x = 1/3 and  x = 1.

问题 3：找出方程的所有解：(7x + 4) ^2/3 = 1。

解决方案：

In the given problem, we can clearly see there is the cube root and square on the variable part so the inverse operation is the cube and square root respectively.

⇒ (7x + 4) = 1^(3/2)

⇒ (7x + 4) = (1³)^(1/2)

⇒ (7x + 4) = 1^(1/2)

So, the square root of 1 is +1 and -1. So we have two cases.

Case 1:

⇒ 7x + 4 = 1

⇒ 7x = 1 – 4

⇒ 7x = -3

⇒ x = -3/7

Case 2: 

⇒ 7x + 4 = -1

⇒ 7x = -1 -4

⇒ 7x = -5

⇒ x = -5/7

So the solution of the given question is  x = -3/7 and  x = -5/7.