This is the basic and conceptual question from linear equations in two variables in which we have been asked to find the numbers if their difference is 5 and their difference between squares is 65.

Kindly solve the above problem by using the properties of linear equations.

RS Aggarwal, Class 10, chapter 3F, question no 7

LetÂ xÂ be the first number andÂ yÂ be second number.

xâˆ’y=5

x2âˆ’y2=65

(xâˆ’y)(x+y)=65....(2)

Now, by dividingÂ (2)Â byÂ (1)Â we get:

x+y=13...(3)

On addingÂ (1)Â andÂ (3)Â we get

2x=18

orÂ x=9

FromÂ (3):9+y=13

OrÂ y=4

Two numbers areÂ 4Â andÂ 9.