Question

The sum of two numbers is 100 and their difference is 37. the difference of their squares is

Answer 1

let the two numbers x and y
x+y=100.......1
x-y=37.........2
from eq 1 we get x=100-y
from eq 2 we get x=37+y
on comparing
37+y=100-y
100-37=2y
63=2y
31.5=y


x-y=37
x=37+y
x=37+31.5
x=68.5
x+y=100
68.5+31.5=100
100=100
hence prooved

Answer 2

Answer:

Let x = the larger number

Let y = the smaller number

x+y = 100

x-y = 37 Add these two equations together.

2x = 137

x = 137/2

y = 100 - x

y = 100 - 137/2

y = 63/2

(137/2)2 - (63/2)2 = 3700