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:

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.