Question

Two numbers multiply together to make 8, but add together to make -6
What are the 2 numbers !?

Answer 1

Answer:

-2, -4

Step-by-step explanation:

let the two numbers be x and y.

according to the question, xy=8

x+y=-6

x=-6-y

y(-6-y)=8

y(y+6)=-8

y^2 +6y +8 = 0

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

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

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

hence either y+2 = 0 or y+4 = 0

hence y= -2 or -4

and x = -4 or -2 respectively.

hence the pair of numbers is -2, -4

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Answer 2

Answer:

- 4 and - 2.

Step-by-step explanation:

Let the required numbers are a and b.

 Their multiplication = 8

            ⇒ ab = 8

  Their sum = - 8

           ⇒ a + b = - 6

⇒ a + b = - 6

⇒ a = - 6 - b

  Hence,

⇒ ab = 8

⇒ ( - 6 - b )b = 8

⇒ - 6b - b^2 = 8

⇒ b^2 + 6b + 8 = 0

⇒ b^2 + ( 4 + 2 )b + 8 = 0

⇒ b^2 + 4b + 2b + 8 = 0

⇒ b( b + 4 ) + 2( b + 4 ) = 0

⇒ ( b + 4 ) ( b + 2 ) =0

⇒ b = - 4 or - 2

   Hence the required numbers are - 4 and - 2.