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Ahat [919]
4 years ago
15

Two positive integers have a sum of 21 and a product of 108. what are the integers

Mathematics
1 answer:
Vitek1552 [10]4 years ago
4 0
X= first integer
21-x= second integer

(x)(21-x)= 108
multiply x by each term in parentheses

21x - x^2= 108
subtract 108 from both sides

21x - x^2 - 108= 0
-x^2 + 21x - 108= 0
multiply whole equation by -1 to eliminate the negative coefficient in the first term

(-1)(-x^2 + 21x - 108)= 0
x^2 - 21x + 108= 0
factor (remember we need #s to add to 21 and multiply to 108)

(x-12)(x-9)= 0

x-12= 0
x= 12

x-9= 0
x= 9

CHECK:
9 + 12= 21
9 * 12= 108

ANSWER: The two positive integers that add to 21 and multiply to 108 are 12 and 9.

Hope this helps! :)
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If Q = {all perfect squares less than 30} and p={ all odd numbers from 1 to 10}
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When Q = {all perfect squares less than 30} and p={ all odd numbers from 1 to 10) Q ∩ P = { 1, 9}

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Set theory simply means the branch of mathematical logic that deals with sets, that can be described as collections of objects.

It should be noted that perfect squares are the numbers that can be divided to give same number.

Q = {all perfect squares less than 30}. This will be 1, 4, 9, 16, 25

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In this case, the common numbers to set of P and Q are 1 and 9.

Therefore, the numbers are 1 and 9 since they're common to both sides.

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