Question

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

Answer 1

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.