Question

the difference of two numbers is 3 and the difference of their square is 69. Find the numbers

Answer 1

let Numbers be X and Y
x-y=3......(1)
X^2-Y^2= 69
(X+Y)(X-Y)= 69
putting value from (1)
3(X+Y)=69
X+Y= 23.....(2)
adding 1 and 2
2X=26
X=13
Y= 13-3=10

Answer 2

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Let the two unknown numbers be x and y respectively.

Then,

According to the question,

x - y = 3 .......(i)

x² - y² = 69 ........(ii)

Now,

From equation (ii) , we get,

x² - y² = 69

=> (x + y)(x - y) = 69

=> (x + y) × 3 = 69. [From (i)]

=> x + y = 69/3

=> x + y = 23 .......(iii)

Now, adding eq. (i) and eq. (ii), we get

x - y = 3
x + y = 23
----------------
2x = 26

=> x = 26/2

=> x = 13

Putting x = 13 in (iii), we get,

x + y = 23

=> 13 + y = 23

=> y = 23 - 13

=> y = 10

Therefore,

The two numbers are 13 and 10 respectively.

HOPE IT HELPS