Question

the difference between two number is16 and the difference bwtween their square is 1312 .find the number ​

Answer 1

Let the numbers be ${\black{x,y}}$

ATP.

x-y=16

$x {}^{2} - {y}^{2}$=1312

(x-y)(x+y)=1312

16 (x+y)=1312

x+y=82

${\black{Simultaneous Equation }}$

x+y=82

x-y=16

.•.2x=98

or, x=49

Putting the value of ${\black{x}}$
We get, y=82-49
Y=33
So one number is ${\green{49}}$
And the other one is${\green{33}}$
HOPE IT HELPS.
${\huge{\red{SOUMOK}}}$

Answer 2

let a and b is two number .

a-b = 16 --------------1

a² - b² = 1312

a² - b² = (a+b)(a-b)

1312 = 16 (a+b)

=> a+b = 1312/16 = 82 ------------2

add both equation ,

a-b = 16 --------------1

a+b = 82 ------------2

--------------------

=> 2a = 98

=> a = 49

b = 49-16 = 33

then no is 33 and 49.