If `A = 8289535 xx 8289545, B = 8289534 xx 8289546, C = 8289533 xx 8289547` Find smallest in A, B and C ?

Options

A. A
B. B
C. C
D. all are same

Answer

To find the smallest among A, B, and C, we need to evaluate each expression step by step.

### Given:
- \( A = 8289535 \times 8289545 \)
- \( B = 8289534 \times 8289546 \)
- \( C = 8289533 \times 8289547 \)

### Step 1: Express A, B, and C in a more manageable form

Notice that:
- \( A = (8289535)(8289545) \)
- \( B = (8289534)(8289546) \)
- \( C = (8289533)(8289547) \)

### Step 2: Rewrite the expressions using a common variable

Let \( x = 8289540 \). Then we can express:
- \( A = (x - 5)(x + 5) = x^2 - 25 \)
- \( B = (x - 6)(x + 6) = x^2 - 36 \)
- \( C = (x - 7)(x + 7) = x^2 - 49 \)

### Step 3: Compare A, B, and C

Now we can compare the three expressions:
- \( A = x^2 - 25 \)
- \( B = x^2 - 36 \)
- \( C = x^2 - 49 \)

### Step 4: Determine the smallest value

Since \( x^2 \) is common in all three expressions, we can focus on the constant terms:
- \( A \) has a constant term of \(-25\)
- \( B \) has a constant term of \(-36\)
- \( C \) has a constant term of \(-49\)

The smallest constant term corresponds to the smallest value:
- \( A > B > C \)

### Conclusion

Thus, the smallest among A, B, and C is:
\[ C = 8289533 \times 8289547 \]