Question

14
The sum of two numbers is 8 and the difference
of their squares is 32. Find the numbers.find the numbers​

Answer 1

Answer:

6 and 2

Step-by-step explanation:

6square-2squares

Answer 2

• The first number = 6
• The second number = 2

Given :

• The sum of the numbers is 8.
• The difference of their squares is 32.

To Find :

The two numbers.

Solution :

Let the number be x and y.

So,

⇒ x + y = 8 [ Equation 1 ]

∵ The sum of numbers = 8

&

⇒ x² - y² = 32   [ Equation 2 ]

∵ The difference of their squares = 32

As we know :

★ a² - b² = (a + b)(a - b)

From Equation 2,

⇒ (x + y)(x - y) = 32

⇒ (8) (x - y) = 32 [ Using Equation 1 ]

We get : (x - y) = 4 as [ Equation 3 ]

• Adding equation 1 & 3

⇒ (x + y)+(x - y) = 8 + 4

⇒  2 x = 12

⇒ x = 6

• Putting the value of x in Equation 1

⇒ 6 + y = 8

⇒ y = 2

Hence,

• The first number = 6
• The second number = 2