In this Question the difference between the numbers and their square is given.

You have to find the numbers.

This is the Important question based on Linear Equations in two Variables Chapter of R.S Aggarwal book for ICSE & CBSE Board.

This is the Question Number 10 Of Exercise 3E of RS Aggarwal Solution.

# The difference between two numbers is 14 and the difference between their squares is 448. Find the numbers.

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Convert this word problem into

algebraic equation.

let the two numbers be x and y

Difference between two numbers is

equal to 14

x – y = 14 —–( 1 )

Difference between their squares is

equal to 448

x^2 – y^2 = 448

( x + y ) ( x – y ) = 448

( x + y ) × 14 = 448

[ from ( 1 ) ]

x + y = 448/ 14

x + y = 32 —-( 2 )

Add equations ( 1 ) and ( 2 ) , we get

2x = 46

x = 46/2

x = 23

Put x = 23 in equation ( 2 )

23 + y = 32

y = 32 – 23

y = 9

Therefore ,

Required two numbers are x = 23

and y = 9