Question

СРОЧНО!!! пожалуйста, помогите

Answer 1

Ответ: x₁=9    y₁=3    x₂=-9     y₂=-3     x₃=3      y₃=9     x₄=-3     y₄=-9.

Объяснение:

$\left \{ {{\frac{x}{y} -\frac{y}{x} =\frac{8}{3} } \atop {x^{2}+y^{2} =90}} \\\left \{ {{\frac{x}{y} -\frac{y}{x} =\frac{8}{3}$

$\frac{x}{y} =t\\t-\frac{1}{t} =\frac{8}{3} |*3t\\3t^{2} -3=8t\\3t^{2} -8t-3=0\\D=100;\sqrt{D}=10\\t_{1} =\frac{x}{y} =3\\x=3y\\(3y)^{2} +y^{2} =90\\9y^{2} +y^{2} =90\\10y^{2} =90 |:10\\y^{2} =9\\y_{1} =3;x_{1} =3*3;x_{1} =9\\ y_{2}=-3;x_{2} =3*(-3);x_{2} =-9.\\t_{2} =\frac{x}{y}= \frac{1}{3}\\ y=3x\\x^{2}+(3x)^{2} =90\\x^{2}+9x^{2} =90\\10x^{2} =90|:10\\x^{2} =9\\x_{3} =3;y_{3} =3*3;y_{3} =9\\x_{4} =-3;y_{4} =3*(-3);y_{4}=-9.$