Question

|x + y - 5| + x² - 6xy + 9y² = 0

Answer 1

Объяснение:

| x + y - 5 | + x² - 6xy + 9y² = 0

| x + y - 5 | + (x+3у)² = 0

| x + y - 5 | = - (x+3y)³

| x + y - 5 | ≥0

-(x+3y)² ≤0

поэтому наше уравнение эквивалентно

системе

{х+у-5=0

{х+3у=0

из второго х= -3у

подставляем его в первое

-3у+у-5=0

-2у=5

у= -2,5

х= -3у = -3•(-2,5) = 7,5

ответ : ( х,у) = ( 7,5 ; -2,5)

Answer 2

The equation you provided is:

|x + y - 5| + x² - 6xy + 9y² = 0

To solve this equation, we need to consider two cases: when |x + y - 5| is positive and when it is negative.

Case 1: |x + y - 5| is positive In this case, the equation becomes:

(x + y - 5) + x² - 6xy + 9y² = 0

Expanding and rearranging the terms, we get:

x² + 2xy - 5x + 9y² - 5y = 0

Factoring the equation, we have:

(x - y)(x + 2y - 5) = 0

From this, we can derive two equations:

1. x - y = 0
2. x + 2y - 5 = 0

Solving equation 1, we get: x = y

Substituting this value into equation 2, we have: x + 2y - 5 = 0 y + 2y - 5 = 0 3y - 5 = 0 3y = 5 y = 5/3

Therefore, one solution for this case is: x = y = 5/3

Case 2: |x + y - 5| is negative In this case, the equation becomes:

-(x + y - 5) + x² - 6xy + 9y² = 0

Expanding and rearranging the terms, we get:

x² - 5x + y² - 5y = 0

Factoring the equation, we have:

(x - 5)(x + y) + y(y - 5) = 0

From this, we can derive two equations:

1. x - 5 = 0
2. x + y = 0

Solving equation 1, we get: x = 5

Substituting this value into equation 2, we have: 5 + y = 0 y = -5

Therefore, another solution for this case is: x = 5, y = -5

In conclusion, the solutions to the equation |x + y - 5| + x² - 6xy + 9y² = 0 are:

1. x = y = 5/3
2. x = 5, y = -5