Question

Tennetiraj sir please answer my question
If x + y = 18 (x and y are positive numbers) and, HCF (x, y) = 2, then, the maximum value of xy will be​

Answer 1

Step-by-step explanation:

Given :-

x + y = 18 (x and y are positive numbers) and, HCF (x, y) = 2

To find :-

Find the maximum value of xy ?

Solution:-

Given that

x+y = 18 ,

Where x and y are positive numbers

=> The sum of x and y = 18

The possible values of x and y are

=> (x,y) = (1,17),(2,16),(3,15),(4,14),(5,13),(6,12),(7,11),(8,10),(9,9),(10,8),(11,7),(12,6),(13,5),(14,4),(15,3),(16,2),(17,1).

Given that HCF (x,y) = 2

The HCF of x and y = 2

The possible values for above condition i.e. The HCF of the values of x and y is 2 are (2,16),(4,14),(8,10),(10,8),(14,4),(16,2)

If x= 2 and y = 16 then xy = 2×16 = 32

If x = 4 and y = 14 then xy = 4×14 = 56

If x = 8 and y = 10 then xy = 8×10 = 80

If x = 10 and y = 8 then xy = 10×8 = 80

If x = 14 and y = 4 then xy = 14×4 = 56

If x = 16 and y = 2 then xy = 16×2 = 32

from above values of xy , 80 is the maximum value .

The maximum value of xy = 80

Answer:-

The maximum value of xy for the given problem is 80