Question

Система х+2/у-3у/х+2=2,ху=16 решите систему уравнений

Answer 1

х + 2/у - 3у/х + 2 = 2
ху = 16

x * xy + 2x - 3y2 + 2xy = 2xy
x = 16/y

x * 16 + 2x - 3y2 + 2 *16 = 2*16
x = 16/y

16 * (16/y) + 2*16/y - 2(16/y)^2 + 32 - 32 = 0

16 * (16/y) + 2*16/y - 2 * 16*16 / y^2 = 0

( (16 * 16 + 2*16)y^2 - 2 * 16*16 ) / y^2 = 0

16 * 16 y^2 + 2*16 y^2 - 2 * 16*16 = 0

16 y^2 + 2 y^2 - 2*16 = 0

18 y^2 = 2*16

9 y^2 = 16

y2 = 16/9

первое решение:
y1 = sqrt( 16 / 9) = 4 / 3
x1 = 16 / (4/3) = 16 * 3 / 4 = 4 * 3 = 12

второе решение:
y2 = - 4 / 3
x2 = -12