Question

find 2 natural numbers sum is 18 and product is 72

Answer 1

factorization of 72
72= 2×2×2×3×3
now,
the product of two natural number is =72
then, 12×2= 72
the sum of two natural number is = 18
the the number are 12+6= 18
so, the natural numbers are 12 and 6 .

Answer 2

Answer:

Let the numbers be x and y

x+y=18

Xy=72

x=18-y

(18-y)y=72

18y-y²-72=0

y²-18y+72=0

a=1,b=-18,c=72

y= -b±√b²-4ac/2a

y= - -18±√-18²-4*1*72/2*1

y=18±√324-288/2

y=18±√36/2

y=18±6/2

so,y=18+6/2 or y=18-6/2

y=24/2 or y= 12/2

y=12 or y=6

substitute y=12 in first equation,

x+y=18

x+12=18

x=18-12

x=6

substitute y=6 in first equation,

x+y=18

x+6=18

x=18-6

x=12

ie, (x=6,y=12) (x=12,y=6)