{16x²+3x-y²=x⁴+8 {3x-y²=8

{ 16x^2 + 3x - y^2 = x^2 + 8,

3x - y^2 = 8;

{ y^2 = 3x - 8,

16x^2 + 3x - (3x - 8) = x^4 + 8;

16x^2 + 3x - 3x + 8 = x^4 + 8;

x^4 - 16x^2 = 0;

x^2(x^2 - 16) = 0;

x^2 = 0 или x^2 - 16 = 0;

x = 0 или x^2 = 16 => x = +-4;

y^2  = 3 * 0 - 8;

y^2 = - 8 - не подходит;

y^2 = 3 * (-4) - 8;

y^2 = -20 - не подходит;

y^2 = 3 * 4 - 8;

y^2 = 12 - 8;

y^2 = 4;

y = +-2;

{x = 4; y = -2,

x = 4; y = 2.

Ответ: (4, -2); (4, 2).