Решите систему уравнений а) {2 ху=5 / 2 х+у=6. б) х-2 у=2 / 2 ху=3

1) y = (6-2x)

2x (6-2x) = 5

12x-4x²-5=0| * (-1)

4x²-12x-5=0

D=√ ((-12) ²-4*4 * (-5)) = √ (144+80) = √224

x1 = ( - (-12) + √224) / 2*4 = (12+√224) / 8 = (12+4√14) / 8

x2 = ( - (-12) - √224) / 8 = (12-√224) / 8 = (12-4√14) / 8

y=5/2x

y1=5/2x1=5/2 * (12+4√14) / 8=5/8 (3+√14) / 8=5 / (3+√14);

y2=5/2x2=5/2 (12-4√14) / 8=5/8 (3-√14) / 8=5 / (3-√14).

2) x = (2+2y)

2y (2+2y) = 3

4y+4y²-3=0

D=√ (4²-4*4 (-3)) = √ (16+48) = √64=8

y1 = (-4+8) / 2*4=4/8=0,5

y2 = (-4-8) / 8=-12/8=-1,5

x1 = (2+2y1) = 2+2*0,5=2+1=3

x2 = (2+2y2) = 2+2 * (-1,5) = 2-3=-1