Question

calculati x,y,xy si x+y din
(x+y)^2+xy =-1
xy-x^2-y^2=-7

Answer 1

Răspuns:

Explicație pas cu pas:

(x+y)²+xy =-1

xy-x²-y²=-7  <=>

x²+2xy+y²+xy = -1

-x²+xy-y² = -7  <=>

x²+3xy+y² = -1

-x²+xy-y² = -7

____________

4xy = -8  => xy = -8:4  => xy = -2  =>

x²-6+y² = -1

-x²-2-y² = -7  <=>

x²+y² = 5

(x+y)² = x²+2xy+y²  => (x+y)² = (x²+y²) + 2xy = 5-4 = 1  =>

x+y = ±√1   => I)  x+y = -1     ;  II)  x+y = 1

I) x + y = -1 ; xy = -2  ; x²+y² = 5   =>

x = 1  ; y = -2 sau  x = -2  ; y = 1

II) x + y = 1 ; xy = -2  ; x²+y² = 5  =>

x = 2  ; y = -1  sau  x = -1  ; y = 2