Question

IV. The sum of two numbers is 28 and difference of their squares is 112.

a) What is the difference of numbers?

b) Find the numbers?​

Answer 1

Answer :-

• Difference of numbers = 4
• numbers = 16 and 12

We have :-

• Sum of two numbers = 28 .
• The deference of their square = 112 .

To find :-

• The difference of the numbers .
• Find the numbers .

Solution :-

• Let first number = x .
• Let second number = y .

A.T.Q, The sum of numbers = 28 .

i.e, x + y = 28 . ................eq.(1)

and, The diffence of their square = 112 .

i.e, x² – y² = 112 . ..............eq.(2)

From eq.(1)

x + y = 28

x = 28 – y ..................eq.(3)

Put the value of x = 28 – y in eq.(2) we get :-

( 28 – y )² – y² = 112

784 + y² – 56y – y² = 112

[ here (+y²) cancelled with (–y²) ]

:⇒ 784 – 56y = 112

:⇒ –56y = 112 – 784

:⇒ – 56y = – 672

[minus will be cancelled from both sides.]

:⇒ 56y = 672

:⇒ y = 672/56

:⇒ y = 12 .

Put the value of y = 12 in eq.(3) we get :-

:⇒ x = 28 – y

:⇒ x = 28 – 12

:⇒ x = 16 .

Therefore,

difference of numbers :-

:⇒ x – y = ?

:⇒ 16 – 12 = 4

The difference of numbers = 4 .

And,

numbers are :- 16 and 12 .