A man is born in the year 1896 A.D. If in the year `x^(2) A.D.` his age is `x-4`, the value of x is

Options

A. 40
B. 44
C. 36
D. 42

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the problem
The man was born in the year 1896 A.D. We need to find the year when his age is \( x - 4 \) and that year is represented as \( x^2 \) A.D.

### Step 2: Set up the equation for age
The age of the man in the year \( x^2 \) A.D. can be calculated as:
\[ \text{Age} = \text{Year} - \text{Birth Year} = x^2 - 1896 \]
According to the problem, this age is also given as \( x - 4 \). Therefore, we can set up the equation:
\[ x^2 - 1896 = x - 4 \]

### Step 3: Rearrange the equation
Now, let's rearrange the equation to bring all terms to one side:
\[ x^2 - x - 1896 + 4 = 0 \]
This simplifies to:
\[ x^2 - x - 1892 = 0 \]

### Step 4: Factor the quadratic equation
Next, we need to factor the quadratic equation \( x^2 - x - 1892 = 0 \). We need two numbers that multiply to -1892 and add to -1. After checking, we find that the numbers 44 and -43 work:
\[ x^2 - 44x + 43x - 1892 = 0 \]
This can be grouped as:
\[ (x - 44)(x + 43) = 0 \]

### Step 5: Solve for \( x \)
Setting each factor to zero gives us:
1. \( x - 44 = 0 \) → \( x = 44 \)
2. \( x + 43 = 0 \) → \( x = -43 \) (not a valid solution since age cannot be negative)

Thus, the only valid solution is:
\[ x = 44 \]

### Conclusion
The value of \( x \) is \( 44 \).

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