Question

х2 + 2у2 + 1 = 27,
3х2 - y2 = 1;
​

Answer 1

Ответ:

Пошаговое объяснение:

$\left \{ {{x^{2} +2y^{2} +1=27} \atop {3x^{2}-y^{2}=1 }} \right. \\\left \{ {{x^{2} +2y^{2} +1=27} \atop {3x^{2}-1=y^{2} }} \right. \\\\x^{2} +2*( 3x^{2}-1)+1=27;\\x^{2} +6x^{2}-2+1=27;\\7x^{2}-28=0;\\\\7(x^{2}-4)=0;\\ 7(x-2)(x+2)=0; \\x_{1}=2; x_{2}=-2\\ 3*(2)^2-1=y_{1} ^{2};\\y_{1} ^{2}=11\\y_{1} =\sqrt{11} \\ 3*(-2)^2-1=y_{2} ^{2};\\y_{2} ^{2}=11\\y_{2} =\sqrt{11} \\\left \{ {{x_{1} =2} \atop {y_{1}=\sqrt{11} }} \right. \\\left \{ {{x_{2} =-2} \atop {y_{2}=\sqrt{11} }} \right.$

Answer 2

{х²+2у²+1=27

{3х²-у²=1 | *2

{х²+2у²=26

{6х²-2у²=2

Делаем сложение:

х²+6х²+2у²-2у²=26+2

{7х²=28

{3х²-у²=1

{х²=4

{3х²-у²=1

{х=-2

{у=-√11

{х=-2

{у=√11

{х=2

{у=-√11

{х=2

{у=√11

Ответ: (-2; -√11); (-2; √11); (2; -√11); (2; √11).