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## Answers

*0 can be written as ( 10 + 10 ).*

*and 10 x 10 = 100.*

*In this case, the product will be maximum.*

*Others numbers maybe =*

** 11 + 9 = 20*

*11 x 9 = 99.*

** 18 + 2 = 20*

*18 x 2 = 36*

**17 + 3. = 20*

*17 x 3 = 51.*

** 16 + 4 = 20*

*16 x 4 = 64*

** 15 + 5 = 20*

*15 x 5 = 75.*

** 14 + 6 = 20*

*14 x 6 = 84.*

** 13 + 7 = 20*

*13 x 7 = 91.*

** 12 + 8 = 20*

*12 x 8 = 96.*

** 11 + 9 = 20.*

*11 x 9 = 99.*

** 10 + 10 = 20.*

*10 x 10 = 100.*

*Hence by hit and trial method it's proved that ( 10 + 10 ) is the answer.*
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Let one part = x

other part = (20-x)

their product, p = x(20-x) = 20x - x²

For the product, p to be maximum

So, product is maximum when we divide 20 into 2 parts as (10,10).

Note: If you want to show that dividing 20 into (10,10) yields maximum product, not minimum; find the second derivative of p. If the value of second derivative at x=10 comes as negative, then it is maximum. (It comes -2, so it is maximum).

other part = (20-x)

their product, p = x(20-x) = 20x - x²

For the product, p to be maximum

So, product is maximum when we divide 20 into 2 parts as (10,10).

Note: If you want to show that dividing 20 into (10,10) yields maximum product, not minimum; find the second derivative of p. If the value of second derivative at x=10 comes as negative, then it is maximum. (It comes -2, so it is maximum).