The product of three integers is –216, but their sum is –23. Which of the following is not one of these three numbers? -2 -12 -6 -9

Respuesta :

Answer:

We can conclude that -6 is not one of these three numbers. So, the actual numbers are:

  • [tex]\left(-2\right)+\left(-12\right)+\left(-9\right)=-23[/tex]
  • [tex]\left(-2\right)\times \left(-12\right)\times \left(-9\right)=-216[/tex]

Step-by-step explanation:

  • The product of three integers is –216.
  • Their sum is –23.

Considering the given numbers

-2 -12 -6 -9

Lets take the three numbers

-2    -12    -9

Taking the sum of -2    -12    -9

[tex]\left(-2\right)+\left(-12\right)+\left(-9\right)[/tex]

[tex]\mathrm{Apply\:rule\:}+\left(-a\right)\:=\:-a[/tex]

[tex]=\:-2-12-9[/tex]

[tex]=-23[/tex]

Therefore, the sum of -2    -12    -9 is -23.

i.e.

[tex]\left(-2\right)+\left(-12\right)+\left(-9\right)=-23[/tex]

Taking the product of -2    -12    -9

[tex]\left(-2\right)\times \left(-12\right)\times \left(-9\right)[/tex]

[tex]\mathrm{Apply\:rule\:}\left(-a\right)\times \left(-b\right)\:=\:a\times \:b[/tex]

as

[tex]\left(-2\right)\times \left(-12\right)=2\times \:12=24[/tex]

so

[tex]=24\times \left(-9\right)[/tex]

[tex]\mathrm{Apply\:rule\:}a\times \left(-b\right)\:=\:-a\times \:b[/tex]

[tex]24\times \left(-9\right)=-24\times \:9=-216[/tex]

Therefore, the product of -2    -12    -9 is -216.

i.e.

[tex]\left(-2\right)\times \left(-12\right)\times \left(-9\right)=-216[/tex]

Thus, we can conclude that -6 is not one of these three numbers. So, the actual numbers are:

  • [tex]\left(-2\right)+\left(-12\right)+\left(-9\right)=-23[/tex]
  • [tex]\left(-2\right)\times \left(-12\right)\times \left(-9\right)=-216[/tex]
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