Given that (x+y+z)(xy+xz+yz)=18 and that x^2(y+z)+y^2(x+z)+z^2(x+y)=6 for real numbers x, y, and z, what is the value of xyz?

4

Step-by-step explanation:

Equation 1

Equation 2

What is the value of where each variable represents a real number?

Let's expand equation 1:

Simplify each term if can:

See if we can factor a little to get some of the left hand side of equation 2:

The first two terms have and if I factored from first two terms I would have which is the first term of left hand side of equation 2.

So let's see what happens if we gather the terms together that have the same variable squared together.

Factor the variable squared terms out of each binomial pairing:

Replace the sum of those first three terms with what it equals which is 6 from the equation 2:

Combine like terms:

Subtract 6 on both sides:

Divide both sides by 3:

b

2

−

b

b

3

+

7

b

2

+

14

b

+

6

%

−

3

b

3

+

7

b

2

+

14

b

+

6

%

step-by-step explanation:

won't that be plagrisim thought?

step-by-step explanation: