Answer :
Step-by-step explanation:
\[
(6 - \sqrt{5})(x + \sqrt{5}) - 11 + y\sqrt{5}
\]
Expanding the expression:
\[
6x + 6\sqrt{5} - x\sqrt{5} - 5 - 11 + y\sqrt{5}
\]
Now, let's group like terms:
\[
(6x - 5) + (6 - x + y)\sqrt{5}
\]
For this expression to be true, both terms must equal zero:
1. \( 6x - 5 = 0 \)
2. \( 6 - x + y = 0 \)
From equation 1, we find \( x = \frac{5}{6} \).
Substituting \( x = \frac{5}{6} \) into equation 2:
\[
6 - \frac{5}{6} + y = 0
\]
\[
\frac{36}{6} - \frac{5}{6} + y = 0
\]
\[
\frac{31}{6} + y = 0
\]
\[
y = -\frac{31}{6}
\]
So, the values of \( x \) and \( y \) that satisfy the expression are \( x = \frac{5}{6} \) and \( y = -\frac{31}{6} \).