Let x,y be the two numbers.
Given that one number is 8 greater than another.
Let x be the smaller number ans y be the greater number.
That is y=x+8. 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+8 here.
x × (x+8) = 84
x²+ 8x -84 = 0.
x²+12x-4x-84 = 0
x(x+12)-4(x+12) =0
(x-4)(x+12)=0
That is x= 4 or -12.
If x=4 , y= 4+ 8 = 12
If x= -12, y= -12+8 = -4
Hence two positive numbers corresponding to given conditions are 4,12.
And two negative numbers corresponding to given conditions are -12,-4.
Step-by-step explanation:
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