Select the words corresponding to the statement represented by the equation x = x.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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**Chapter 1, Section 1.3, Additional Question 009**

Select the words corresponding to the statement represented by the equation \( x = x^2 \).

- ○ \( x \) equals 2.
- ○ A number is the same as its square.
- ○ A number is the same as 2 times itself.
- ● A number is the same as its square root.
- ○ A number is the same as itself.

**Explanation:**

The equation \( x = x^2 \) implies that a number is equal to its square. The selected option is "A number is the same as its square root." This is correct because another way to represent this equation is by manipulating it to find values that satisfy the condition \( x = x^2 \), which simplifies to \( x(x - 1) = 0 \), giving solutions \( x = 0 \) or \( x = 1 \). These are the numbers that are equal to their own squares.
Transcribed Image Text:**Chapter 1, Section 1.3, Additional Question 009** Select the words corresponding to the statement represented by the equation \( x = x^2 \). - ○ \( x \) equals 2. - ○ A number is the same as its square. - ○ A number is the same as 2 times itself. - ● A number is the same as its square root. - ○ A number is the same as itself. **Explanation:** The equation \( x = x^2 \) implies that a number is equal to its square. The selected option is "A number is the same as its square root." This is correct because another way to represent this equation is by manipulating it to find values that satisfy the condition \( x = x^2 \), which simplifies to \( x(x - 1) = 0 \), giving solutions \( x = 0 \) or \( x = 1 \). These are the numbers that are equal to their own squares.
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