If `a^(3) = 1 + 7, 4^(2) = 1 + 5 + b`, `5^(3) = 1 + 8 + c`, then the value of a + b + c is

Options

A. 130
B. 128
C. 120
D. 126

Answer

To solve the problem step by step, we will analyze each equation given in the question and find the values of \(a\), \(b\), and \(c\).

### Step 1: Solve for \(a\)
Given the equation:
\[ a^3 = 1 + 7 \]

Calculating the right side:
\[ 1 + 7 = 8 \]
Thus, we have:
\[ a^3 = 8 \]

Now, we can find \(a\) by taking the cube root of both sides:
\[ a = \sqrt[3]{8} = 2 \]

### Step 2: Solve for \(b\)
Next, we look at the second equation:
\[ 4^2 = 1 + 5 + b \]

Calculating \(4^2\):
\[ 4^2 = 16 \]

Now substituting this into the equation:
\[ 16 = 1 + 5 + b \]

Calculating the right side:
\[ 1 + 5 = 6 \]
So we have:
\[ 16 = 6 + b \]

Now, we can solve for \(b\):
\[ b = 16 - 6 = 10 \]

### Step 3: Solve for \(c\)
Now, we will solve the third equation:
\[ 5^3 = 1 + 8 + c \]

Calculating \(5^3\):
\[ 5^3 = 125 \]

Now substituting this into the equation:
\[ 125 = 1 + 8 + c \]

Calculating the right side:
\[ 1 + 8 = 9 \]
So we have:
\[ 125 = 9 + c \]

Now, we can solve for \(c\):
\[ c = 125 - 9 = 116 \]

### Step 4: Calculate \(a + b + c\)
Now that we have found \(a\), \(b\), and \(c\):
- \(a = 2\)
- \(b = 10\)
- \(c = 116\)

We can now find \(a + b + c\):
\[ a + b + c = 2 + 10 + 116 \]
Calculating this gives:
\[ a + b + c = 128 \]

### Final Answer
The value of \(a + b + c\) is:
\[ \boxed{128} \]