Answer :
Answer:
To find the value of \( P \) in the expression \( \sqrt{2 + \sqrt{3}} = \sqrt{3} + \sqrt{3 - a + a\sqrt{3}} \), we proceed as follows:
Let's equate the given expression with \( P \):
\[ \sqrt{2 + \sqrt{3}} = \sqrt{3} + \sqrt{3 - a + a\sqrt{3}} \]
To solve for \( a \), we'll square both sides to eliminate the square roots:
\[ 2 + \sqrt{3} = (\sqrt{3} + \sqrt{3 - a + a\sqrt{3}})^2 \]
Expand the right-hand side:
\[ (\sqrt{3} + \sqrt{3 - a + a\sqrt{3}})^2 = 3 + 3 - a + a\sqrt{3} + 2\sqrt{3(3 - a + a\sqrt{3})} \]
Now, equate both sides and simplify to find \( a \). After solving the resulting equation, you can substitute the value of \( a \) back into the expression for \( P \):
\[ P = \sqrt{3} + \sqrt{3 - a + a\sqrt{3}} \]
This process involves algebraic manipulation and solving equ