Question

the difference between two positive number is 5and the sum of squares is 73 find the product of these numbers​

Answer 1

Answer:

The product of the two numbers is 24.

Given:

• The difference between two positive number is 5.

• The sum of their squares is 73.

To find:

• The product of the two numbers.

Solution:

Let the two positive numbers be x and y.

According to the first condition.

》x - y = 5...(1)

According to the second condition.

》x² + y² = 73...(2)

Squaring equation (1), we get

》x² + y² - 2xy = 25...(3)

Subtract equation (3) from equation (2), we get

⠀x² + y² + 0xy = 73

-

⠀x² + y² - 2xy = 25

___________________

⠀⠀⠀=> 2xy = 48

⠀⠀⠀=> xy = 48/2

⠀⠀⠀=> xy = 24

Therefore, the product of the two numbers is 24.

____________________________

Extra information:

• a² + b² = (a - b)² + 2ab

• (a + b)² = (a - b)² + 4ab

• (a - b)² = (a + b)² - 4ab

• a³ + b³ = (a + b) (a² - ab + b²)

• a³ - b³ = (a - b) (a² + ab + b²)

Answer 2

Answer:

let numbers=x,y

therefore x-y=5,x=y+5

x2+y2=73

(x-y)2+2xy=73

(x-y)2=73-2xy

(5)2=73-2xy

73-25=2xy

48=2xy

48/2=xy

24=xy

therefore product of numbers is 24