2 number that the product 891 differance of the 2 numbers are 6

Question

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Answer 1

Let m and n be the two numbers.  We have two unknowns (m and n) so we need two equations to solve for m and n:

m*n = 891             [Product of the two numbers is 891]

m-n = 6                  [Difference of the two numbers is 6]

 

From the second equation, m = 6+n.  Now let's substitute 6+n in place of m in the first equation:

 

m*n = 891

(6+n)*n = 891          [Substituted 6+n in place of m]

6n + n² = 891

n² + 6n - 891 = 0

Factors to:

(n+33)(n-27) = 0

n = -33, 27

 

Solve for m:

m = 6 + n

m= 6 + (-33) = -27

m= 6 + (27) = 33

 

There are two solution sets, (m,n) = (-27, -33) and (33,27)

 

CHECK:

m*n=891

(-27)*(-33) = 891

891 = 891

 

(33)*(27) = 891

891 = 891

 

m-n = 6

(-27)-(-33) = 6

-27 + 33 = 6

6 = 6

 

33 - 27 = 6

6=6