Question

Vreau si eu sa ma ajutati,va rog la punctele d,e,f. Dau coroana!

Answer 1

d) (x+y)^2 + 6 + xi = 5(x +y)+(y+1)i
x^2 + 2xy + y^2 +6 +xi = 5x+5y+yi+i
x^2+y^2+2xy-5x-5y+6 = yi+i-xi
x^2+y^2+2xy-5x-5y+6 = (y-x+1)i
x^2+y^2+2xy-5x-5y+6 + (x-y-1)i = 0
=>   (1)    x^2+y^2+2xy-5x-5y+6 =0
       (2)    x-y-1=0 => x = y+1
Inlocuim in relatia (1) x = y+1 si avem
(y+1)^2+y^2+2(y+1)y-5(y+1)-5y+6 = 0
y^2 +2y +1 + y^2 +2y^2+2y-5y-5-5y+6 = 0
4y^2 -6y +2 = 0 / :2
2y^2-3y+1=0
Δ = 9-8=1
y1 = (3+1)/4 = 1  => x1 = y1+1 = 2
y2 = (3-1)/4 = 1/2 => x2 = y2+1 = 3/2