Question

√6+ x - 3 √3y + 4 = -10, 4√3y+ 4 - 5 √6 + x = 6;​

Answer 1

$\displaystyle\bf\\\left \{ {{\sqrt{6+x} -3\sqrt{3y+4}=-10} \atop {4\sqrt{3y+4} -5\sqrt{6+x} =6}} \right. \\\\\\\left \{ {{\sqrt{6+x} -3\sqrt{3y+4}=-10} \ |\cdot 5 \atop { -5\sqrt{6+x} +4\sqrt{3y+4} =6}} \right. \\\\\\+\left \{ {{5\sqrt{6+x} -15\sqrt{3y+4}=-50} \atop { -5\sqrt{6+x} +4\sqrt{3y+4} =6}} \right. \\----------------\\-11\sqrt{3y+4} =-44\\\\\sqrt{3y+4} =4\\\\(\sqrt{3y+4} )^{2} =4^{2} \\\\3y+4=16\\\\3y=12\\\\\boxed{y=4}\\\\\\\sqrt{6+x} =3\sqrt{3y+4} -10=3\cdot 4-10=12-10=2$

$\displaystyle\bf\\(\sqrt{6+x} )^{2}=2^{2} \\\\6+x=4\\\\\boxed{x=-2}\\\\Otvet \ : \ \Big(-2 \ ; \ 4\Big)$