Respuesta :
the two numbers are 24 & 8 .
Step-by-step explanation:
Here we have , The difference between two natural numbers is 16. The product of these natural numbers is 192.We need to Find these numbers. Let's find out:
Let two numbers be x & y , So The difference between two natural numbers is 16 , i.e.
⇒ [tex]x-y = 16[/tex] ...........(1)
The product of these natural numbers is 192 , i.e.
⇒ [tex]xy=192[/tex]
We know that , [tex](x+y)^2 = (x-y)^2+4xy[/tex] i.e.
⇒ [tex](x+y)^2 = (16)^2+4(192)[/tex]
⇒ [tex](x+y)^2 = 1024[/tex]
⇒ [tex]x+y = \pm 32[/tex] { Since sum can't be negative as both numbers are positive }
⇒ [tex]x+y = 32[/tex] ........(2)
Adding (1) & (2) :
⇒ [tex](x-y)+(x+y) = 16+32[/tex]
⇒ [tex]2x=48[/tex]
⇒ [tex]x=24[/tex]
So , y = 32-x = 32-24 = 8
Therefore , the two numbers are 24 & 8 .
