An important and exam oriented question from linear equations in two variables in which we have to find the numbers if difference between two numbers is 14 and the difference between their squares is 448
RS Aggarwal, Class 10, chapter 3E, question no 10
Let us consider,
First number =x and
Second number =y
(Assume y is smaller)
As per the statement,
x−y=14....(1)
and x²−y²=448
(x+y)(x−y)=488
(x+y)×14=448
x+y=32....(2)
Adding (1) from (2)
2x=46 or x=23
Subtracting (1) from (2)
2y=18 or y=9
Answer
Numbers are 23 and 9