Respuesta :
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.
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
