Question 1148245
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Not at all clear because of the poor English....<br>
"...so that the product of ... is a maximum 10."<br>
Are you looking for ANY two number with a sum of 9 for which the product is LESS THAN OR EQUAL TO 10?  Or does the product have to be EQUAL to 10?<br>
And by "numbers" do you mean integers? or can they be any numbers?<br>
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Tell your lecturer that "...is a maximum 10" is not good English if what he means is that the product is anything less than 10.<br>
If "numbers" means integers, then there are only a small number of possibilities, and they are easy to check; there is clearly only one solution: 8 and 1.<br>
If the numbers are integers, the problem then seems of little value, since you don't learn anything from solving it.<br>
Since the problem apparently asks to find one solution, 8 and 1 is certainly the simplest answer (and the only answer, if the numbers are integers).<br>
A more useful problem -- that would teach the student something about problem solving -- would be to find the complete solution set of values for x that make the product x(9-x)^2 less than or equal to 10.<br>