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.
⇒ [tex]x(y) = -24[/tex]
two numbers adds up to (-10):
Two numbers are x and y , and there addition is -10 i.e.
⇒ [tex]x+y = -10[/tex] . .............. (1)
Let's solve this :
We know that , [tex](x+y)^2 = x^2 +y^2 +2xy[/tex]
⇒ [tex](x+y)^2 = x^2 +y^2 +2xy[/tex]
⇒ [tex](-10)^2 = x^2 +y^2 +2(-24)[/tex]
⇒ [tex]100 = x^2 +y^2 -48[/tex]
⇒ [tex]x^2 +y^2 =148[/tex]
Now,
⇒ [tex](x-y)^2 = x^2 +y^2 -2xy[/tex]
⇒ [tex](x-y)^2 = (148) -2(-24)[/tex]
⇒ [tex](x-y)^2 = (148) +48=196 = 14^2[/tex]
⇒ [tex]x-y = 14[/tex] .......... (2)
Let's solve equation 1 & 2 by adding (1)+(2):
⇒ [tex](x+y)+(x-y) = -10 +14[/tex]
⇒ [tex]2x=4[/tex]
⇒ [tex]x=2[/tex]
Putting value of [tex]x=2[/tex] in [tex]x-y = 14[/tex] :
⇒ [tex]2-y = 14[/tex]
⇒ [tex]y = -12[/tex]
Therefore, two numbers multiply into (-24) and adds up to (-10) are 2 & -12.
