One number is 5 greater than another. The product of the numbers are 84. Find both the two positive and two negative sets of numbers.

GIVEN

one number is greater than the other by 5.

the product of both are 84.

find out the number.

To proof =

let assume that one number be x

other number be x+5

the equation becomes

⇒ x (x+8) = 84

⇒ x²+5x-84 = 0

⇒ x² + 12x-7x-84 = 0

⇒ (x-7) (x+12) = 0

⇒x=7, x=-12

now the positive numbers are 7 and 12

now the negative numbers are - 12 and - 7

hence proved

Let x, y be the two numbers.

Given that one number is 5 greater than another.

Let x be the smaller number ans y be the greater number.

That is y=x+5. Let this be the first equation.

And also given that product of the two numbers is 84.

That is x*y = 84, let us plugin y=x+5 here.

x * (x+5) = 84

x^2 + 5x - 84 = 0.

x^2+12x-7x-84 = 0

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

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

That is x = 7 or - 12.

If x=7, y = 7+5=12.

If x=-12, y = - 12+5 = - 7.

Hence two positive numbers corresponding to given conditions are 7,12.

And two negative numbers corresponding to given conditions are - 12,-7.