Question

Пожалуйста помогите!!!, в долгу не останусьпомогите решить систему(x^2-2xy+y^2=25(2x^2-2xy-y^2=11ВОТ МОТИВАЦИИ!!! 60 баллов :))

Answer 1

$\left \{ {{x^2-2xy+y^2=25} \atop {2x^2-2xy-y^2=11}} \right. \left \{ {{(x-y)^2=5^2} \atop {2x^2-2xy-y^2=11}} \right. \left \{ {{x-y=б5} \atop {2x^2-2xy-y^2=11}} \right. \\ \left \{ {{x-y=-5} \atop {2x^2-2xy-y^2=11}} \right. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left \{ {{x-y=5} \atop {2x^2-2xy-y^2=11}} \right. \\ \left \{ {{y=x+5} \atop {2x^2-2x(x+5)-(x+5)^2=11}} \right. \ \ \ \ \left \{ {{y=x-5} \atop {2x^2-2x(x-5)-(x-5)^2=11}} \right.$
$\left \{ {{y=x+5} \atop {2x^2-2x^2-10x-x^2-10x-25=11}} \right. \left \{ {{y=x-5} \atop {2x^2-2x^2+10x-x^2+10x-25=11}} \right. \\ \left \{ {{y=x+5} \atop {x^2+20x+36=0}} \right. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left \{ {{y=x-5} \atop {x^2-20x+36=0}} \right. \\ \left \{ {{y_1=3 \ y_2=-13 } \atop {x_1=-2 \ x_2=-18}} \right. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left \{ {{y_3=-3 \ y_4=13} \atop {x_3=2 \ x_4=18}} \right. \\ (-2;3) \ (-18;-13) \ (2;-3) \ (18;13)$

Answer 2

Solving the System of Equations

To solve the system of equations (x^2 - 2xy + y^2 = 25) and (2x^2 - 2xy - y^2 = 11), we can use the method of substitution or elimination. Let's proceed with the substitution method to find the values of x and y that satisfy both equations.

Substitution Method

We can start by solving one of the equations for one variable and then substituting that expression into the other equation.

First, let's solve the second equation (2x^2 - 2xy - y^2 = 11) for y: ``` 2x^2 - 2xy - y^2 = 11 - y^2 - 2xy + 2x^2 = 11 - y^2 - 2xy = 11 - 2x^2 y^2 + 2xy = 2x^2 - 11 y^2 = 2x^2 - 2xy - 11 y^2 = 2x^2 - 2x^2 - 11 y^2 = -11 y = ±√(-11) ``` Now, we have the value of y in terms of x.

Next, we can substitute the expression for y into the first equation (x^2 - 2xy + y^2 = 25): ``` x^2 - 2x(±√(-11)) + (-11) = 25 x^2 - 2x(±√(-11)) - 11 = 25 x^2 - 2x(±√(-11)) = 36 x^2 - 2x(±√(-11)) - 36 = 0 ``` We can solve this quadratic equation to find the possible values of x.

Conclusion

By using the substitution method, we can find the values of x and y that satisfy both equations. This approach will help us solve the given system of equations and earn the 60 points motivation!