Question

Решите уравнение(189-190) 40 .! 1) 2) 3) 4)

Answer 1

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

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