The product of two number is 24 and the sum of their squares is 52. Find their sum .
A .5
B.10
C. 15
D.20.

Options

A. D
B. C
C. B
D. A

Answer

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

1. **Define the Variables**: Let the two numbers be \( x \) and \( y \).
- We know from the problem that:
- \( xy = 24 \) (the product of the two numbers)
- \( x^2 + y^2 = 52 \) (the sum of their squares)

2. **Use the Identity for the Sum of Squares**: We can use the identity:
\[ x^2 + y^2 = (x + y)^2 - 2xy \]
This allows us to relate the sum of squares to the sum of the numbers and their product.

3. **Substitute Known Values**: Substitute \( x^2 + y^2 \) and \( xy \) into the identity:
\[ 52 = (x + y)^2 - 2 \cdot 24 \]
Simplifying this gives:
\[ 52 = (x + y)^2 - 48 \]

4. **Rearrange the Equation**: Add 48 to both sides:
\[ 52 + 48 = (x + y)^2 \]
\[ 100 = (x + y)^2 \]

5. **Take the Square Root**: To find \( x + y \), take the square root of both sides:
\[ x + y = \sqrt{100} \]
\[ x + y = 10 \]

6. **Conclusion**: The sum of the two numbers is \( 10 \).

Thus, the answer is **B. 10**.