Вправи 401 - 467 » 415 (1)

415. Знайдіть (х/у)2, якщо: 1) (〖4x〗^(-2)+ y^(-2))/(x^(-2)+ 〖5y〗^(-2) ) = 1; (4/x^2 + 1/y^2 )/(1/x^2 + 5/y^2 ) = 1; ((〖4y〗^2+ x^2)/(x^2 y^2 ))/((y^2+ 〖5x〗^2)/(x^2 y^2 )) = 1; (〖(4y〗^2+ x^2) • x^2 y^2)/(x^2 y^2 •〖(y〗^2+〖5x〗^2)) = 1; (〖4y〗^2+ x^2)/(y^2+ 〖5x〗^2 ) = 1; y2 + 5x2 = 4y2 + x2; 5x2 – x2 = 4y2 – y2; 4x2 = 3y2 |: 4y2; (x/y)2 = 3/4; (x/y)2 = 0,75.