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

Step-by-step 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.