Объяснение:
5/4 и 3/2 = (3 * 2) /(2 * 2) = 6/4; б) 2/3 = (2 * 5)/(3 * 5) = 10/15 и 2/15 в) 7/15 = (7 * 3)/(15 * 3) = 21/45 и 5/9 = (5 * 5)/(9 * 5) = 25/45; г) 1/6 = (1 * 5)/(6 * 5) = 6/30 и 3/10 = (3 * 3)/(10 * 3) = 9/30; д) 1/3 = (1 * 6)/(3 * 6) = 6/18 и 5/18 е) 5/8 = (5 * 3)/(8 * 3) = 15/24 и 2/3 = (2 * 8)/(3 * 8) = 16/24; ж) 1/2 = (1 * 15)/(2 * 15) = 15/30 и 2/15 = (2 * 2)/(15 * 2) = 4/30; з) 5/12 = (5 * 5)/(12 * 5) = 25/60 и 7/15 = (7 * 2)/(15 * 2) = 14/30; и) 3/10 = (3 * 10)/(10 * 10) = 30/100 и 33/100.
{x^2+y^2=58
{xy=21
{ x²+y² =58 ; xy=21. ⇔ {(x+y)² -2xy =58 ; xy=21. ⇔ {(x+y)² -2*21=58 ; xy=21.⇔
{(x+y)²=10² ; xy=21.⇔{ x+y=±10 ; xy=21. ⇔ совокупности 2-х систем
* * * [ { x+y= -10 ; xy=21 ; { x+y= -10 ; xy=21.
a) { x+y= -10 ; xy=21.
x и y можно рассматривать как корни уравнения
t² + 10t +21 =0 ⇔ [ t= -3 ; t = -7.
* * * иначе { y= -10 - x ; x (-10 -x )=2.⇔{ y= -10 - x ; x²+10x +21 =0 * * *
(-7 ; -3) или (-3 ; -7).
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b) { x+y= 10 ; xy=21.
t² - 10t +21 =0 ⇔ [ t= 3 ; t = 7.
(3 ; 7) или (7 ; 3)}.
ответ: { (-7 ; -3) , (-3 ; -7), (3 ; 7) , (7 ; 3) }.