Question

ДАЮ 70 балов решите уровнение способами из 5-9 классов Х^2 + Y^2+ Z^2 = 12 XY+ XZ +YZ = 12

Answer 1

Ответ:

по сути вот

Пошаговое объяснение:

Выполни такие преобразования:

1) умножь первое уравнение на 2;

2) умножь второе уравнение на 2;

3) вычти из первого уравнения второе,

4) сгруппируй слагаемые так:

(x^2-2xy+y^2)+(y^2-2yz+z^2)+(z^2-2zx+x^2)=0

дальше

(x-y)^2+(y-z)^2+(z-x)^2=0

{ x-y=0; y-z=0; z-x=0

x=y=z

3x^2=12

x=+-2

Ответ: (2;2;2), (-2;-2;-2)

Answer 2

Solving the Equation

To solve the equation X^2 + Y^2 + Z^2 = 12XY + XZ + YZ = 12, we can use various methods depending on the level of mathematics. Here, I will provide two methods: one suitable for students in grades 5-9 and another for a more advanced approach.

Method 1: Suitable for Grades 5-9

To solve the equation using a method suitable for students in grades 5-9, we can use substitution. Let's solve it step by step:

1. Start by isolating one variable in terms of the others. Let's isolate Z in terms of X and Y: - From the equation X^2 + Y^2 + Z^2 = 12XY + XZ + YZ = 12, we can rewrite it as Z^2 - XZ - YZ = 12XY - X^2 - Y^2. - Rearrange the equation to isolate Z: Z^2 - XZ - YZ = 12XY - X^2 - Y^2. - Factor out Z: Z(Z - X - Y) = 12XY - X^2 - Y^2. - Divide both sides by (Z - X - Y): Z = (12XY - X^2 - Y^2) / (Z - X - Y).

2. Substitute the value of Z in terms of X and Y back into the original equation: - Replace Z with (12XY - X^2 - Y^2) / (Z - X - Y) in the equation X^2 + Y^2 + Z^2 = 12XY + XZ + YZ = 12. - Simplify the equation.

3. Solve the resulting equation for X and Y using algebraic methods such as factoring, completing the square, or using the quadratic formula.

Method 2: Advanced Approach

To solve the equation using a more advanced approach, we can use the quadratic formula. Let's solve it step by step:

1. Rearrange the equation X^2 + Y^2 + Z^2 = 12XY + XZ + YZ = 12 to isolate one variable: - We can isolate Z by subtracting XZ and YZ from both sides: Z^2 - XZ - YZ = 12XY.

2. Apply the quadratic formula to solve for Z: - The quadratic formula is given by Z = (-b ± √(b^2 - 4ac)) / (2a), where the equation is in the form az^2 + bz + c = 0. - In our case, a = 1, b = -X - Y, and c = 12XY. - Substitute these values into the quadratic formula and simplify.

3. Solve the resulting equation for X and Y using algebraic methods such as factoring, completing the square, or using the quadratic formula.

Please note that the specific values of X and Y are not provided in the question, so we cannot provide the exact solutions. However, by following the steps outlined above, you should be able to solve the equation using either method.

I hope this helps! Let me know if you have any further questions.