Respuesta :

mavila18

Answer:

[tex]a+\sqrt{a-1}[/tex]

Step-by-step explanation:

The conjugate of an expression of the form:

[tex]z=a+b[/tex]      (1)

is another expression of the form:

[tex]z=a-b[/tex]     (2)

In the same way, if your expression is [tex]z=a-b[/tex], the conjugate is [tex]z=a+b[/tex].

You have the following expression:

[tex]a-\sqrt{a-1}[/tex]

by comparing with the equations (1) and (2) you can take a=a and b=√a-1. Thus, you have the expression z = a - b. The conjugate is z = a + b. Then, you can conclude that the conjugate is:

[tex]a+b=a+\sqrt{a-1}[/tex]

onyebuchinnaji

Answer:

the conjugate of  [tex]a -\sqrt{a-1} \ = a + \sqrt{a -1}[/tex]

Step-by-step explanation:

Given;

[tex]a - \sqrt{a-1}[/tex]

Conjugate of [tex]a -\sqrt{x} \ \ \ is \ \ a \ + \ \sqrt{x}[/tex]

let (a - 1) = x

a - √x = a + √x

∴ [tex]a -\sqrt{a-1} \ = a + \sqrt{a -1}[/tex]

Therefore, the conjugate of  [tex]a -\sqrt{a-1} \ = a + \sqrt{a -1}[/tex]

Check

[tex](a -\sqrt{a-1}) *(a+\sqrt{a-1} ) = a^2 + \ a\sqrt{a-1}\ - \ a\sqrt{a-1} - (a-1)\\\\(a -\sqrt{a-1}) *(a+\sqrt{a-1} ) = a^2 - (a-1)\\\\(a -\sqrt{a-1}) *(a+\sqrt{a-1} ) = a^2 -a+1[/tex]

The result is a rational number, hence [tex]a + \sqrt{a-1} \ \ is \ \ conjugate \ of \ \ a -\sqrt{a-1}[/tex]

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