Answer :
Answer:
Step-by-step explanation:To find \( x^2 + \frac{1}{x^2} \) given \( x = \sqrt{6} + \sqrt{8} \), we first need to determine \( x^2 \) and \( \frac{1}{x^2} \).
First, let's find \( x^2 \):
\[ x = \sqrt{6} + \sqrt{8} \]
Squaring both sides, we get:
\[ x^2 = (\sqrt{6} + \sqrt{8})^2 \]
Expanding the square using the identity \((a + b)^2 = a^2 + 2ab + b^2\):
\[ x^2 = (\sqrt{6})^2 + 2(\sqrt{6})(\sqrt{8}) + (\sqrt{8})^2 \]
\[ x^2 = 6 + 2(\sqrt{6} \cdot \sqrt{8}) + 8 \]
\[ x^2 = 6 + 2(\sqrt{48}) + 8 \]
\[ x^2 = 6 + 2 \cdot 4\sqrt{3} +