Answer:
A. 12 and 8
Step-by-step explanation:
Let x be the larger positive number and y be the smaller positive number.
Since, the difference between these number is 4,
⇒ x - y = 4,
⇒ x = 4 + y ------(1)
Also, the product of these number is 96,
⇒ xy = 96
From equation (1),
\((4+y)y = 96\)
\(4y+y^2=96\)
\(y^2+4y-96=0\)
\(y^2+12y-8y-96=0\)
\(y(y+12)-8(y+12)=0\)
\((y-8)(y+12)=0\)
By zero product property,
y-8=0 or y+12=0
y = 8 or y = - 12( not possible )
Again from equation (1),
x = 4 + 8 = 12,
Hence, the numbers are 12 and 8,
Option A is correct.
