Question

Решите уравнение(189-190)Дам 40 баллов.Срочно!
1)$x^{4} -34 x^{2} =225=0$
2)$x^{4}-20 x^{2} +100=0$
3)$x^{4}+3 x^{2} -28=0$
4)$x^{4}-4 x^{2} -24=0$

Answer 1

$1); ; x^4-34x^2+225=0; ,\\x^2=17-8=9; ,; ; x^2=17+8=25\\x_{1,2}=pm 3; ,; x_{3,4}=pm 5\\2); ; x^4-20x^2+100=0; ,\\(x^2-10)^2=0; ; to ; ; x^2=10; ,; ; x_{1,2}=pm sqrt{10}\\3); ; x^4+3x^2-28=0; ,\\x^2=-7; ; net; reshenij,; t.k.; x^2 geq 0\\x^2=4; ; to ; ; x_{1,2}=pm 2$

$4); ; x^4-4x^2-24=0; ,\\D/4=4+24=28; ,\\x^2=2-frac{}{}sqrt{28}=2-2sqrt7 textless 0; ; net; reshenij\\x^2=2+2sqrt7; ; to ; ; x_{1,2}=pm sqrt{2+2sqrt7}=sqrt{2(1+sqrt7)}$