Question

If the sum of two numbers are 14 and difference between their square were 28. Find the numbers

Answer 1

Answer:

x=8

y=6

Step-by-step explanation:

Let x be the first number

y be the second number

From the given data,

x+y=14 ..eqn(1)

x²-y²=28 ..eqn(2)

By algebraic expressions,

a²-b²=(a-b)(a+b)

Then,

x²-y²=14

(x-y)(x+y)=28

Dividing by eqn 1,

(x-y)=2

By Substitution method,

2x=16

x=8

By the value of x,

y=6

Answer 2

Given :

• Sum of two numbers = 14
• Difference between their squares = 28

To find :

• The two numbers

Solution :

Let the two numbers be x and y.

• First number = x
• Second number = y

1st condition,

• x + y = 14 -----(1)

2nd condition,

• x² - y² = 28 ------(2)

Using identity,

• (x + y)(x - y) = x² - y²

⠀⠀⠀⠀⠀⠀⇒ x² - y² = 28

⠀⠀⠀⠀⠀⠀⇒ (x + y)(x - y) = 28

⠀⠀⠀⠀⠀⠀⇒ Substituting (1) in x + y

⠀⠀⠀⠀⠀⠀⇒ 14(x - y) = 28

⠀⠀⠀⠀⠀⠀⇒ x - y = 28/14

⠀⠀⠀⠀⠀⠀⇒ x - y = 2

• x - y = 2 ------(3)

Solving (1) and (3)

⠀⠀⠀⠀⠀⠀x + y = 14

⠀⠀⠀⠀⠀⠀x - y = 2

⠀⠀⠀⠀⠀__________

⠀⠀⠀⠀⠀⠀2x = 16

⠀⠀⠀⠀⠀__________

⠀⠀⠀⠀⠀⠀⇒ 2x = 16

⠀⠀⠀⠀⠀⠀⇒ x = 16/2

⠀⠀⠀⠀⠀⠀⇒ x = 8

The value of x = 8.

Substitute the value of x in (1).

⠀⠀⠀⠀⠀⠀⇒ x + y = 14

⠀⠀⠀⠀⠀⠀⇒ 8 + y = 14

⠀⠀⠀⠀⠀⠀⇒ y = 14 - 8

⠀⠀⠀⠀⠀⠀⇒ y = 6

The value of y = 6.

∴ The two numbers are,

• 8 and 6