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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?

worty [1.4K]

Answer:

4

Step-by-step explanation:

$(x+y+z)(xy+xz+yz)=18$ Equation 1

$x^2(y+z)+y^2(x+z)+z^2(x+y)=6$ Equation 2

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

Let's expand equation 1:

$(x+y+z)(xy+xz+yz)=18$

$x(xy)+x(xz)+x(yz)+y(xy)+y(xz)+y(yz)+z(xy)+z(xz)+z(yz)=18$

Simplify each term if can:

$x^2y+x^2z+xyz+y^2x+xyz+y^2z+xyz+z^2x+z^2y=18$

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

The first two terms have $x^2$ and if I factored $x^2$ from first two terms I would have $x^2(y+z)$ 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.

$x^2y+x^2z+y^2x+y^2z+z^2y+z^2x+xyz+xyz+xyz=18$

Factor the variable squared terms out of each binomial pairing:

$x^2(y+z)+y^2(x+z)+z^2(y+x)+xyz+xyz+xyz=18$

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

$6+xyz+xyz+xyz=18$

Combine like terms:

$6+3xyz=18$

Subtract 6 on both sides:

$3xyz=12$

Divide both sides by 3:

$xyz=4$

4 0

3 years ago

PLS help me Order four and seven tenths repeating, negative four and eight ninths, 490%, and −4.9 from least to greatest.

Digiron [165]

The order from least to greatest negative four and seven tenths repeating, negative four and eight ninths, 490%, and −4.9 from least to greatest is; option A

−4.9,
negative four and eight ninths
four and seven tenths repeating
490%,

<h3>Ascending order</h3>

four and seven tenths repeating

= 4.77777777

negative four and eight ninths

= -4 8/9

= -4.888888888888888

490%

= 490/100

= 4.9

−4.9

Rearranging from least to greatest (ascending order)

-4.9
-4.888888888888888
4.77777777
4.9

Learn more about ascending order;

brainly.com/question/12783355

#SPJ1

6 0

2 years ago

What is the price per lb of brand X coffee if 3 lb were mixed with 9 lb of brand Y coffee which costs $18/lb to make 12 lb of Ka

Georgia [21]

Answer:

$14 per lb

Step-by-step explanation:

Given:

Brand Y = $18 / lb
Special Blend = $17 / lb

Let x be the price per lb of brand X coffee

3 lbs of brand X coffee + 9 lb of brand Y coffee = 12 lbs of special blend

⇒ 3x + 9(18) = 12(17)

⇒ 3x + 162 = 204

⇒ 3x = 42

⇒ x = 14

Therefore, brand X costs $14 per lb

4 0

2 years ago

Read 2 more answers

Classify each as an expression or an equation.

fenix001 [56]

Answer:

1. equation

2. equation

3. expression

4. expression

explanation is that an equation has an equal sign and an expression doesnt .

5. equation

Step-by-step explanation:

6 0

3 years ago

What is the relationship between the value of the digit 3 in 4,231 and in the value of the digit 3 in the number 3,421?

Marina CMI [18]

Answer:

A.

In 4231, the value of the digit 3 is 110 less than the value of the digit 3 in 3421.

Step-by-step explanation:

We can see that the value of 3 In 4231 is in ten while the value of 3 in 3421 is in thousands.

So to get the actual division factor, let's take 3300 and divide it by 30,

3300/30 = 110

So it's clear already, that the value of 3 in 4231 is 110 times less to the value in 3421

4 0

3 years ago