Question

Решите уравнение используя способ введения новой переменной (у^2-8)^2+2(y^2-8)-8=0 (Помогите)

Answer 1

${y}^{4} - 16 {y}^{2} + 64 + 2 {y}^{2} - 16 - 8 = 0 \\ {y}^{4} - 14 {y}^{2} + 40 = 0$
замена y²=t
$t \geqslant 0$
$t1.2 = \frac{14 + - 6}{2}$
$t1 = 10 \\ t2 = 4$
${y}^{2} = 10 \\ y =+- \sqrt{10}$
${y}^{2} = 4 \\ y = +-2$

Answer 2

$y^2-8=t;\ t^2+2t-8=0;\ (t+4)(t-2)=0;\ \left [ {{t=-4} \atop {t=2}} \right.$

$\left [ {{y^2-8+4=0} \atop {y^2-8-2=0}} \right. \Leftrightarrow \left [ {{y=\pm 2} \atop {y=\pm\sqrt{10}}} \right.$