Question

ПОМОГИТЕ ПОЖАЛУЙСТА АААААААА даю 40 баловввввв​

Answer 1

Ответ:

Объяснение:

$\displaystyle\\\left \{ {{\dfrac{x}{y}+\dfrac{y}{x} =\dfrac{34}{15} } \atop {x^2+y^2=34}} \right. ~~~~~~~~~x\neq 0;y\neq 0\\\\\\\left \{ {{\dfrac{x^2+y^2}{xy}=\dfrac{34}{15} } \atop {x^2+y^2=34}} \right. ;\left \{ {{\dfrac{1}{xy}=\dfrac{1}{15} } \atop {x^2+y^2=34}} \right. ;\left \{ {{xy=15 } \atop {x^2+y^2=34}} \right. \\\\\\\left \{ {{y=\dfrac{15}{x} } \atop {x^2+y^2=34}} \right. ;\left \{ {{y=\dfrac{15}{x} } \atop {x^2+\dfrac{225}{x^2} =34}} \right.$

$x^4-34x^2+225=0\\x^4-25x^2-9x^2+225=0\\x^2(x^2-25)-9(x^2-25)=0\\(x^2-9)(x^2-25)=0\\(x-3)(x+3)(x-5)(x+5)=0\\x_1=3;y_1=5\\x_2=-3;y_2=-5\\x_3=5;y_3=3\\x_4=-5;y_4=-3\\\\Otvet:(3;5);(-3;-5);(5;3);(-5;-3)$