Find two numbers summing to be 16.8 whose product is maximal?

Question

Can you please tell me if my answer to this math question is right?

My answer:
8.4 and 8.4 because, when added, they equal 16.8.
Of all the numbers that can be added together to equal 16.8 and then multiplyed together, 8.4 times 8.4 will give the greatest product - 70.56

Answer 1

Yes, you're correct.
.

Answer 2

the equation you are after is this :

when is (y-x) multiplied by x equal to the biggest figure, where y is the figure you are giving (16.8 in this case)

well when x is half of y the equation will work out at :
(y/2) multipled by (y/2), which equals :
y squared / 4
this value (y squared / 4) gives the value of 70.56 which is the value you gave, and the maximum product always occurs when the value is half of the original figure

so for example if u wanted 2 figures that add to 100 to multiply and make the largest figure it would happen when 50 x 50 = 2500

if you wanted a more complex challenge try doing it with complex figures and see what happens then, will a similar rule still be followed?

or even try seeing which 3 figures when added to form a certain value produces the largest product? will the 3 figures be one third of the original value you give?

Answer 3

:) Nothing left to add to this question. You have totally summed it up beautifully. This answer must be a product of your sheer genius. No one will be able to take anything away from you. However, puns found too repititiously in one of the answers may cause divisions among your visitors. :)

Answer 4

you're right..

-x^2+16.8x

maxima= -b/2ac
=16.8/2
=8.4

Answer 5

YEOWSER, yeowser. This can be shown be to true for any real number.

Answer 6

Yes it is.

Answer 7

correct

Answer 8

yes, you are right

Answer 9

You've answered it, and I agree.