The value of `[(0.87)^(2)+(0.13)^(2)+(0.87)xx(0.26)]^(2013)` is

Options

A. 0
B. 2013
C. 1
D. `-1`

Answer

To solve the expression \([(0.87)^{2} + (0.13)^{2} + (0.87) \times (0.26)]^{2013}\), we can follow these steps:

### Step 1: Identify the components of the expression
We have:
- \(A = 0.87\)
- \(B = 0.13\)

### Step 2: Rewrite the expression
We can use the identity \(A^2 + B^2 + 2AB = (A + B)^2\) to rewrite the expression. First, we need to express \(0.87 \times 0.26\) in terms of \(A\) and \(B\):
\[ 0.87 \times 0.26 = 0.87 \times (2 \times 0.13) = 2 \times 0.87 \times 0.13 \]

### Step 3: Substitute into the expression
Now we can rewrite the original expression:
\[ (0.87)^{2} + (0.13)^{2} + 2 \times 0.87 \times 0.13 \]
This can be recognized as:
\[ (0.87 + 0.13)^{2} \]

### Step 4: Simplify the expression
Now we simplify \(0.87 + 0.13\):
\[ 0.87 + 0.13 = 1 \]
Thus, we can rewrite the expression as:
\[ (1)^{2} \]

### Step 5: Raise to the power of 2013
Now we raise this result to the power of 2013:
\[ (1)^{2013} = 1 \]

### Final Answer
Therefore, the value of \([(0.87)^{2} + (0.13)^{2} + (0.87) \times (0.26)]^{2013}\) is:
\[ \boxed{1} \]