Question

The difference of two numbers is 2 & the difference of their square is 44 . Find the numbers ​

Answer 1

Answer:

x - y = 2

x2 - y2 = 44

(x + y)(x - y) = 44

(x + y)2 = 44

x + y = 22

x - y = 2

2x = 24

x = 12

Answer 2

• Given

• Difference of two numbers = 2
• Difference of their square = 44

• To find

• The numbers

• Solution

Let the numbers be x and y.

• First number = x
• Second number = y

As given in the question,

• x - y = 2 ----(1)
• x² - y² = 44

x² - y² = 44

• Expanding x² - y²

★ Identity to be used :-

• (x - y)(x + y) = x² - y²

⟶ x² - y² = 44

⟶ (x - y)(x + y) = 44

• Substitute 2 in x - y.

⟶ 2(x + y) = 44

⟶ x + y = 44/2

⟶ x + y = 22 ----(2)

Now, we have the value of the sum of the two numbers, the difference of the two numbers.

Solving (1) and (2).

x + y = 22

x - y = 2

_________

2x = 24

__________

⟶ 2x = 24

⟶ x = 24/2

⟶ x = 12

The value of x = 12

Substituting the value of x in (1)

⟶ x - y = 2

⟶ 12 - y = 2

⟶ -y = 2 - 12

⟶ -y = - 10

⟶ y = 10

The value of y = 10

_______________________________

Let's verify :-

Substituting the value of x and y in (1)

⟶ x - y = 2

⟶ 12 - 10

⟶ 2

Hence, verified.