Question

решить систему уравнений:

1)  4x^2-y=2

     3x-2y=-1

2)   x/y=1/3

       x^2+y^2=50

Answer 1

$left { {{4 x^{2} -y=2} \ atop {3x-2y=-1}} right. \ \ left { {{y=4 x^{2} -2} \ atop {3x-2(4 x^{2} -2)=-1}} right. \ \ left { {{y=4 x^{2} -2} \ atop {3x-8 x^{2} +4+1=0}} right. \ \ left { {{y=4 x^{2} -2} \ atop {8 x^{2} -3x-5=0}} right. \ \ \ D=3^2+4*8*5=169=13^2 \ \ x_1= frac{3+13}{2*8}=1 \ \ x_2= frac{3-13}{2*8} =-frac{5}{8} =-0.625 \ \ y_1=4*1-2=2 \ \ y_2= 4*(- frac{5}{8} )^2-2=- frac{7}{16} =-0,4375$

Ответ (1;  2); (-0,625; -0,4375)

$left { {{ frac{x}{y} = frac{1}{3} } atop { x^{2} +y^2=50}} right. \ \ left { {{y=3x} atop {x^2+y^2=50}} right. \ \ left { {{y=3x} atop {x^2+(3x)^2=50}} right. \ \ left { {{y=3x} atop {x^2+9x^2=50}} right. \ \ left { {{y=3x} atop {10x^2=50}} right. \ \ 10 x^{2} =50 \ \ x^{2} =5 \ \ x_1= sqrt{5} \ \ x_2=- sqrt{5} \ \ y_1= 3 sqrt{5} \ \ y_2=-3 sqrt{5}$

Ответ (√5; 3√5), (-√5; -3√5)