Question

Sum of two numbers is 20 and their product is 75. Then sum of their squares is

• A. 225
• B. 240
• C. 250
• D. 260

Hint:

Remember identity: $x^2 + y^2 = (x+y)^2 - 2xy$.

Answer 1

The Correct Option is C

Let's solve the problem step by step:

1. We are given that the sum of two numbers is 20 and their product is 75. Let the two numbers be \(x\) and \(y\).
2. According to the problem, the sum of the numbers is given as: \(x + y = 20\)
3. The product of the numbers is given as: \(xy = 75\)
4. We need to find the sum of the squares of these numbers. It is given by: \(x^2 + y^2\)
5. This can be calculated using the identity: \((x + y)^2 = x^2 + y^2 + 2xy\)
6. Substitute the known values into the identity: \((20)^2 = x^2 + y^2 + 2 \times 75\)
7. Simplify the equation: \(400 = x^2 + y^2 + 150\)
8. Subtract 150 from both sides to solve for \(x^2 + y^2\): \(x^2 + y^2 = 400 - 150 = 250\)

Therefore, the sum of the squares of the numbers is 250.