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Q: What are two numbers such that one number is 2 larger than 5 times the second number algebraically find two numbers so that their product is a minimum?

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a=3b

Suppose the smaller of the two numbers is x. Then the larger is x + 16 and their product is x*(x+16) = x2 + 16x This has its minimum when 2x = -16 or x = -8 When x = -8, the two numbers are -8 and 8 and their product is -64.

The two numbers are 3 and 5 and so 5 is the larger number

9

4,6,8,10

"Either" is used for two. I'll assume that you mean "larger than ANY of them". The following applies to ANY real numbers.For TWO numbers, the product is larger than either of them if both numbers are greater than one. For THREE numbers, the product is larger than any of them if the two numbers OTHER than the largest number have a product greater than one. For example: 0.5, 3, 5 The largest number here is 5; the product of the OTHER two is 0.5 x 3 = 1.5. Or here is an example with integers: -5, -3, 10 The product of the "other two" numbers is 15, which is larger than one - so the product of all three is larger than the largest number (and therefore, larger than ANY of them). Another example: -5, 1, 10 The product of the two numbers OTHER than the largest is -5 x 1 = -5; since this is NOT greater than 1, the product of all three is NOT greater than any of the numbers. This reasoning can be extended to four or more numbers. For 4 numbers: If the product of all three numbers OTHER than the largest one is GREATER than one, then the product of ALL FOUR numbers is greater than ANY of them.

five

9

9

7

5 - the other number is 3

6 times 7 = 42 and so 7 is the larger number

12 and 12, whose squares will be 144 each. If either of the numbers is smaller than 12, then the other will be larger than 12 and its square will be larger than 144.

In 'normal' arithmetic, there is no solution of 3 consecutive odd numbers where the product of the smaller two is 22 less than that of the larger two. For instance difference in products for 1-3-5 is 12, for 3-5-7 it is 20, and for 5-7-9 it is 28. The series steps by 8 integers for each set of 3 odd numbers investigated.

7 x 9 = 63 Therefore, the larger number is 63.

10, -9 sum is 1 product is -90. any two numbers one positive one negative, positive has to be larger

They are 6, 8, 10 and 12.

Any product of two or more odd numbers that are larger than 1. For example, 33 = 3*11 is odd and composite.

The numbers are: 378 and 42 because (9*42)*42 = 15876

The two numbers are 9 and 11, or indeed -9 and -11. Therefore, the larger number is 11 (or -9).

6 x 8 = 48 10 x 12 = 120 120 - 48 = 72

It is also a number. It can be smaller than, equal to or larger than either of the two numbers.

The product of a positive and negative number is always negative The sum of a positive and negative number depends on which one is larger; subtract the two numbers and take the sign of the larger

A trick for figuring out squares of larger numbers that is sometimes helpful: if you can write the numbers as the product of two different numbers, then you can square those two numbers and multiply that to find the square of the original. 602 = 102*62 = 100*36 = 3600

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