Question

What are two numbers that add together to make -7 and that multiply to make 6

Answer 1

-2 and -4 this is the answer

Answer 2

These two numbers are -1 and -6 respectively.

Explanation:

Suppose first number is x and the second number is y.

Then according to question-

( x + y ) = -7 ..............................(i)

x × y = 6 ................................(ii)

As we know that-

`(x - y)^(2)` =
`(x + y )^(2)  - 4 x y` .......................(iii)

Now, Putting values of equation (i), (ii) in equation (iii)-

We get,

`( x - y )^(2)` =
`( - 7 )^(2)` - 4 × 6

`( x - y )^(2)` = 49 - 24

`( x - y )^(2)` = 25

( x - y ) =
`√(25)`

( x - y ) = 5..........................(iv)

After adding equation (i) and (iv)-

( x + y ) = -7

( x - y ) = 5

2 x = -2

x = -2 /2

x = -1

Now put x = -1 in equation (i)-

We get,

y = -7 - x

y = -7 - (- 1)

y = - 7 + 1

y = -6

Hence the both numbers x and y are -1, -6 respectively.