Question

Vrog frumos imi trebuie urgent!
Aflati valoarea raportului algebric:x^2-xy+y^2 supra x^2-y^2+1 pentru:
a)x=1+radical din2,y=radical din2-1
b)x=radical din5-2,y=radical din5+2.

Answer 1

raport = (x² - xy + y²)/(x² -y² +1)
a)  x = 1+√2    x² = 3+2√2    y = √2 - 1      y² = 3 - 2√2     xy = (√2 +1)(√2-1) = 1
raport = (3+2√2 - 1 + 3 -2√2) / (3+2√2 - 3 +2√2 +1) = 5·/(4√2+1) = 5(4√2 -1)/33
b) x = √5 -2    x² = 9 - 4√5    y =√5 +2    y² = 9 +4√5    xy = 1
raport = (9 - 4√5 - 1+9+ 4√5) / (9 - 4√5 - 9 - 4√5 +1) = 17/(1- 8√5)=-17(8√5 +1)/319