Answer :
Answer:
a² = 45 - 20√5.
Step-by-step explanation:
To find a², we need to square the expression for a:
a = 5 - 2√5
a² = (5 - 2√5)²
Expanding the square, we get:
a² = (5 - 2√5)(5 - 2√5)
= 25 - 4√5(5) + 4(5)
= 25 - 20√5 + 20
= 45 - 20√5
So, a² = 45 - 20√5.
Answer:
Step-by-step explanation:Let's start by expressing \( a \) in a form that allows us to find \( a^2 \). Given:
\[ a = 5 - 2\sqrt{5} \]
We need to find \( a^2 \). To do this, we'll square both sides of the equation:
\[ a^2 = (5 - 2\sqrt{5})^2 \]
Now, let's expand the right side of the equation using the formula \((x - y)^2 = x^2 - 2xy + y^2\):
\[ (5 - 2\sqrt{5})^2 = 5^2 - 2 \cdot 5 \cdot 2\sqrt{5} + (2\sqrt{5})^2 \]
Calculate each term separately:
\[ 5^2 = 25 \]
\[ 2 \cdot 5 \cdot 2\sqrt{5} = 20\sqrt{5} \]
\[ (2\sqrt{5})^2 = 4 \cdot 5 = 20 \]
Putting it all together:
\[ (5 - 2\sqrt{5})^2 = 25 - 20\sqrt{5} + 20 \]
Combine the constant terms:
\[ 25 + 20 = 45 \]
Thus, we have:
\[ a^2 = 45 - 20\sqrt{5} \]
Therefore, the value of \( a^2 \) is:
\[ a^2 = 45 - 20\sqrt{5} \]