wykaż że jeśli : x+y=-6 i x^2+y^2=27,to x*y=4,5
x-y=5 i x*y=20,to x^2+y^2=65
x+y=-6 i x^2+y^2=27,to x*y=4,5
x + y = -6
x^2 + y^2 = 27
x + y = -6 / *()^2
(x + y)^2 = (-6)^2
x^2 + 2xy + y^2 = 36
--------------------------------- odejmujesz
2xy = 9 / : 2
xy = 4,5
x * y = 4,5
x - y = 5 / ()^2
x * y = 20
(x - y)^2 = 25
x * y = 20 / * 2
x^2 - 2xy + y^2 = 25
2xy = 40
-------------------------------- dodajesz
x^2 + y^2 = 65
pozdrawiam.
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x+y=-6 i x^2+y^2=27,to x*y=4,5
x + y = -6
x^2 + y^2 = 27
x + y = -6 / *()^2
(x + y)^2 = (-6)^2
x^2 + 2xy + y^2 = 36
x^2 + 2xy + y^2 = 36
x^2 + y^2 = 27
--------------------------------- odejmujesz
2xy = 9 / : 2
xy = 4,5
x * y = 4,5
x-y=5 i x*y=20,to x^2+y^2=65
x - y = 5 / ()^2
x * y = 20
(x - y)^2 = 25
x * y = 20 / * 2
x^2 - 2xy + y^2 = 25
2xy = 40
-------------------------------- dodajesz
x^2 + y^2 = 65
pozdrawiam.