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**Let the Numbers be x and y respectively**

**According to the given question**

**xy = 84**

**x = 84/y ----------------1**

**x - y= 5 ----------------2**

**Substituting The Value of x in equation 2**

x - y = 5

84 - y = 5

----

y

84 - y² = 5

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y

84 - y² = 5y

y² + 5y - 84 = 0

y² - 7y + 12y - 84 = 0

y(y - 7) + 12(y - 7) = 0

(y - 7)(y +12) = 0

**y = 7 or y = -12**

**In the Question it is Specified that the numbers are positive so y can be negative**

**So,**

**y = 7**

**Substitute the value of y In Equation 2**

x - y = 5

x - 7 = 5

**x = 12**

**Therefore**

**The Numbers are 12 and 7**

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