Question

What two numbers multiply into (-24) and adds up to (-10)?

Answer 1

Two numbers multiply into (-24) and adds up to (-10) are 2 & -12

Explanation:

Here we need to find two numbers , with the following info:

Let us assume that two numbers are x & y .

two numbers multiply into (-24):

Two numbers are x and y , and there multiply is -24 i.e.

⇒
`x(y) = -24`

two numbers adds up to (-10):

Two numbers are x and y , and there addition is -10 i.e.

⇒
`x+y = -10` . .............. (1)

Let's solve this :

We know that ,
`(x+y)^2 = x^2 +y^2 +2xy`

⇒
`(x+y)^2 = x^2 +y^2 +2xy`

⇒
`(-10)^2 = x^2 +y^2 +2(-24)`

⇒
`100 = x^2 +y^2 -48`

⇒
`x^2 +y^2 =148`

Now,

⇒
`(x-y)^2 = x^2 +y^2 -2xy`

⇒
`(x-y)^2 = (148) -2(-24)`

⇒
`(x-y)^2 = (148) +48=196 = 14^2`

⇒
`x-y = 14` .......... (2)

Let's solve equation 1 & 2 by adding (1)+(2):

⇒
`(x+y)+(x-y) = -10 +14`

⇒
`2x=4`

⇒
`x=2`

Putting value of
`x=2` in
`x-y = 14` :

⇒
`2-y = 14`

⇒
`y = -12`

Therefore, two numbers multiply into (-24) and adds up to (-10) are 2 & -12.