To find the conjugate of the expression [tex]\(4 - \sqrt{x+5}\)[/tex], we need to apply the definition of a conjugate in algebra. The conjugate of any expression of the form [tex]\(a - b\)[/tex] is [tex]\(a + b\)[/tex].
Here, the expression is [tex]\(4 - \sqrt{x+5}\)[/tex]. To form its conjugate, we need to replace the minus sign with a plus sign. Thus, the conjugate of [tex]\(4 - \sqrt{x+5}\)[/tex] would be:
[tex]\[4 + \sqrt{x+5}\][/tex]
To summarize:
- The original expression is [tex]\(4 - \sqrt{x+5}\)[/tex].
- Its conjugate replaces the [tex]\(-\)[/tex] with [tex]\(+\)[/tex].
- Therefore, the conjugate is [tex]\(4 + \sqrt{x+5}\)[/tex].
Given the choices:
A. [tex]\(4 - \sqrt{x-5}\)[/tex]
B. [tex]\(4 - \sqrt{x+5}\)[/tex]
C. [tex]\(4 + \sqrt{x-5}\)[/tex]
D. [tex]\(4 + \sqrt{x+5}\)[/tex]
The correct choice is:
D. [tex]\(4 + \sqrt{x+5}\)[/tex]
