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Which choice is the conjugate of the expression below when [tex]x \geq 5[/tex]?

[tex]\sqrt{x-5} - 2[/tex]

A. [tex]\sqrt{x+5} - 2[/tex]

B. [tex]\sqrt{x-5} - 2[/tex]

C. [tex]\sqrt{x-5} + 2[/tex]

D. [tex]\sqrt{x+5} + 2[/tex]

Sagot :

GinnyAnswer
To find the conjugate of the expression [tex]\(\sqrt{x-5} - 2\)[/tex], we need to form an expression where the sign between the two terms is changed. Here, the original expression is:

[tex]\[ \sqrt{x-5} - 2 \][/tex]

The conjugate of an expression of the form [tex]\(a - b\)[/tex] is [tex]\(a + b\)[/tex]. Denote [tex]\(a = \sqrt{x-5}\)[/tex] and [tex]\(b = 2\)[/tex].

By changing the sign from minus to plus, the conjugate expression becomes:

[tex]\[ \sqrt{x-5} + 2 \][/tex]

Therefore, the correct choice is:

[tex]\[ \text{C. } \sqrt{x-5} + 2 \][/tex]

Thus, the conjugate of [tex]\(\sqrt{x-5} - 2\)[/tex] is [tex]\(\sqrt{x-5} + 2\)[/tex]. The answer is C.
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