Question

Pair of numbers whos product is 8 and sum is -6

Answer 1

Let x,y are numbers

x+y=-6. -->y=-(x+6)

xy=8.

x[-(x+6)]=8

x(-x-6)=8

-x square - 6x= 8

Moving all terms to RHS

x square + 6x +8 = 0

x square +2x + 4x + 8=0

x(x+2) + 4(x+2) = 0

(x+2)(x+4)=0

x=-2,-4

if x = -2

(-2)y=8... from xy=8

y=-4

that's it the pair of numbers are -2 and -4

Answer 2

Let the numbers be x and y.

the product of the numbers =8

the sum of the numbers= -6

xy=8. (1)

x+y=-6. (2)

x=-6-y = -(6+y). (3)

by substituting (1) in (3)

(-6-y)(y)= 8

-6y-y^2=8

-(6y+y^2+8)=0

6y+y^2+8=0

by factorizing the quadratic equation

y^2+4y+2y+8=0

y(y+4)+2(y+4)=0

(y+2)(y+4)=0

y=-2,-4

if y=-2,-4 then x=-4 or -2

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