Question

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.

Answer 1

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

Answer 2

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.