What will come in place of question mark(?) in the following questions?
`(sqrt5-2)^2=?-sqrt(80)`

Options

A. `4sqrt5 +4`
B. `4sqrt5`
C. `9-4sqrt5`
D. 9

Answer

To solve the equation \((\sqrt{5} - 2)^2 = ? - \sqrt{80}\), we will follow these steps:

### Step 1: Expand the left side of the equation
We start by expanding \((\sqrt{5} - 2)^2\) using the formula \((a - b)^2 = a^2 - 2ab + b^2\).

\[ (\sqrt{5} - 2)^2 = (\sqrt{5})^2 - 2 \cdot \sqrt{5} \cdot 2 + 2^2 \]

### Step 2: Calculate each term
Now, we calculate each term in the expansion:
- \((\sqrt{5})^2 = 5\)
- \(2^2 = 4\)
- \(-2 \cdot \sqrt{5} \cdot 2 = -4\sqrt{5}\)

Putting it all together, we have:

\[ (\sqrt{5} - 2)^2 = 5 - 4\sqrt{5} + 4 \]

### Step 3: Combine like terms
Now, we combine the constant terms:

\[ 5 + 4 - 4\sqrt{5} = 9 - 4\sqrt{5} \]

So, we have:

\[ (\sqrt{5} - 2)^2 = 9 - 4\sqrt{5} \]

### Step 4: Set the equation
Now, we set the expanded expression equal to the right side of the original equation:

\[ 9 - 4\sqrt{5} = ? - \sqrt{80} \]

### Step 5: Simplify \(\sqrt{80}\)
Next, we simplify \(\sqrt{80}\):

\[ \sqrt{80} = \sqrt{16 \cdot 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5} \]

### Step 6: Substitute back into the equation
Now we substitute \(\sqrt{80}\) back into the equation:

\[ 9 - 4\sqrt{5} = ? - 4\sqrt{5} \]

### Step 7: Solve for ?
To find the value of \(?\), we can add \(4\sqrt{5}\) to both sides of the equation:

\[ 9 - 4\sqrt{5} + 4\sqrt{5} = ? \]

This simplifies to:

\[ 9 = ? \]

### Final Answer
Thus, the value that comes in place of the question mark (?) is:

\[ \boxed{9} \]

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