Question

The sum of the squares of two numbers is 41. The difference of the squares of these numbers is 9 What are the numbers?​

Answer 1

Answer:

Explanation:

Given :

• Sum of the square of two numbers is 41.
• The difference of the squares of these numbers is 9.

To Find :

• Numbers.

Solution :

Let, first number be "R" and second number be "S" respectively.

Case (I) : Sum of the square of two numbers is 41.

=> R² + S² = 41______(1)

Case (II) : The difference of the squares of these numbers is 9.

=> R² - S² = 9_______(2)

From equation (1) & (2),

R² + S² = 41

R² - S² = 9

+ + +

_________

2R² = 50

=> R² = 50/2

=> R² = 25

=> R = √25

=> R = 5

Put R = 5 in eqn. (1),

=> 5² + S² = 41

=> 25 + S² = 41

=> S² = 41 - 25

=> S² = 16

=> S = √16

=> S = 4

So,

• First number = R = 5
• Second number = S = 4

Hence :

The first number and second number is 5 and 4 respectively.