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## Answers

__Let the numbers be a and b__

__Therefore,a+b=27__

__or,a=27-b..............(1)__

__ab=182__

__putting the value of a as 27-b from...(1) we get,__

__(27-b)b=182__

__or,27b-b²-182=0__

__or,b²-27b+182=0__

__or,b²-13b-14b+182=0__

__or,b(b-13)-14(b-13)=0__

__or,(b-14)(b-13)=0__

__Hence, either b-14=0 or b-13=0__

__or,either b=14 or b=13__

__Since a=27-b__

__a= either 27-14 or 27-13__

__or,a= either 13 or 14.__

__Therefore, either__

__a and b are 13 and 14 or__

__a and b are 14 and 13 .__

__By both ways , we can see that the 2 numbers are 14 and 13.__

__Ans:The numbers are 14 and 13.__### This Is a Certified Answer

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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

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

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.