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Let the two numbers be A and B.

A + B = 27

A B = 182 = 13*7*2*1

Let us find A and B by factors method.

A and B can be possibly from the list of the following :

1, 2, 7, 13, 14, 26, 91, 182

Take the left most factor and right most factor and then check if sum is 27. Continue to the next factor from left. So check 1 & 182 ; 2 & 91 ; 7 & 26 ;

If you choose 13 and 14 as A and B, then A+B = 27 and AB = 182.

So A = 13 and B = 14

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Another way:

A+ B = 27 so A = 27 - B

A B = (27 - B)B = 27 B - B² = 182

B² - 27 B + 182 = 0

B = [ 27 + - √ ( 27² - 4*182) ] / 2 = (27+1) / 2 or (27-1)/2

B = 14 or 13

So A = 27 - B = 13 or 14.

A + B = 27

A B = 182 = 13*7*2*1

Let us find A and B by factors method.

A and B can be possibly from the list of the following :

1, 2, 7, 13, 14, 26, 91, 182

Take the left most factor and right most factor and then check if sum is 27. Continue to the next factor from left. So check 1 & 182 ; 2 & 91 ; 7 & 26 ;

If you choose 13 and 14 as A and B, then A+B = 27 and AB = 182.

So A = 13 and B = 14

================================

Another way:

A+ B = 27 so A = 27 - B

A B = (27 - B)B = 27 B - B² = 182

B² - 27 B + 182 = 0

B = [ 27 + - √ ( 27² - 4*182) ] / 2 = (27+1) / 2 or (27-1)/2

B = 14 or 13

So A = 27 - B = 13 or 14.