评估 √81 – | -8 + 17 | + 3
代数表达式是一种有助于使用字母表表示数字而不指定其实际值的表达式。用于隐藏实际值的字母称为变量。
常量实际上是表达式中的数字。表达式可以由变量和常量组成,也可以由变量组成,也可以由常量组成。当一个变量乘以一个常数时,它被称为系数。
The algebraic expression consists of operators like addition, subtraction, division, multiplication, and many more. The algebraic expressions are always commutative, associative, and distributive.
e.g.
Given that: 4y – 5.
Here:
- y is the variable,
- 4 and 5 are constants.
- 4y is the coefficient.
代数表达式的类型
- 单项式表达式:只有一项的表达式。示例:3x、x、4a。
- 二项式表达式:具有两个项的表达式。示例:4x + 7 有两个项 4x 和 7。
- 多项式表达式:具有两个以上项的表达式是多项式表达式。示例:ax+b+cy 具有三个项。
- 数值表达式:只有常量但没有变量的表达式。示例:15/2,3+6
- 变量表达式:包含变量和常量的表达式。示例:5 年 + 33
绝对值
The absolute value is always positive irrespective of the sign of the complex number. It is just a magnitude. It is often known by the name of modulus and is often represented by | x | where x is any value. The absolute value of any number is always the positive and the absolute value of a negative number is also positive.
例如找到-6-8的绝对值
我们知道:-6-8 = – 14
| -14 | = 14
公式
代数表达式的一些公式:
- |-a| = |一个| =一个
- √(a+b) ² = ±(a+b)
- √(ab) ² = ±(ab)
评估:√81 - | -8 +17 | + 3
解决方案:
The √81 has two values +9 or -9
| -8 +17 | =| 9 | = 9
Case 1: when we consider the positive square root that is +9
9 – 9 + 3 = 3
Case 2: When we consider the negative square root that is -9
-9 – 9 + 3 = -15
So there are two answers of the numerical expression 3 and -15
类似问题
问题1:求∛{( 64 ) +33 + | 的值√81|}。
解决方案:
∛{64} = 4
√81 = ± 9
| ±9 | = 9
So evaluating the expression we get
4 + 9 + 33 = 46
问题 2:使用 x=1, y=0 评估表达式; 4y+ x +2xy+1。
解决方案:
Putting the values of x and y in the expression as,
4y + x +2xy+1
we get
4(0) + 1 + 2(0)(1) +1 = 2
问题 3:评估√ (64) +| -7 – 17 |
解决方案:
√64 = ±8
|-7-17|= |-24|= 24
Case 1: When +8 is considered
8 + 24 = 32
Case 2: When -8 is considered
-8 + 24 = 16
The answers are 16 and 32.
问题 4:查找 | -6 × 5 + 7| + 3。
解决方案:
We evaluate the modulus first
| -30 + 7| = | -23 | = 23
23 + 3 = 26