Question

Решите уравнение |x^5-6x^2+9x-6|=|x^5-2x^3+6x^2-13x+6| и найдите сумму квадратов всех его решений.

Answer 1

$\left | x^5-6x^2+9x-6 \right |=\left | x^5-2x^3+6x^2-13x+6 \right |\\\left ( x^5-6x^2+9x-6 \right )^2=\left ( x^5-2x^3+6x^2-13x+6 \right )^2\\\left ( 2x^5-2x^3-4x \right )\left ( 2x^3-12x^2+22x-12 \right )=0\\x\left ( x^4-x^2-2 \right )\left ( x^3-6x^2+11x-6 \right )=0\\x\left ( x^2+1 \right )\left ( x^2-2 \right )\left ( x-1 \right )\left ( x-2 \right )\left ( x-3 \right )=0\\x\left ( x^2-2 \right )\left ( x-1 \right )\left ( x-2 \right )\left ( x-3 \right )=0\\x=\left \{ \pm \sqrt{2};0;1;2;3 \right \}$

$A=\left ( \sqrt{2} \right )^2+\left ( -\sqrt{2} \right )^2+1+4+9\\A=18$

Answer 2

//////////////////////////////////////