Х^4-11х^2+30=0 Х*(х+1)-(х+2)(х+3)+8=х*(х+4)-(х+5)(х+2)

x²=y y²-11y+30=0 D=121-4*30=1 y₁=(11-1)/2=5 y₂=(11+1)/2=6 x₁ ₂=+-√5 x₃ 4=+-√6 2) Х*(х+1)-(х+2)(х+3)+8=х*(х+4)-(х+5)(х+2) x²+x-(x²+2x+3x+6)+8=x²+4x-(x²+5x+2x+10) x²+x-x²-5x-6+8=x²+4x-x²-7x-10 -4x+2=-3x-10 -3x+4x=2+10 x=12

[latex]x^4-11x^2+30=0\\\\t=x^2 \geq 0\; ,\; \; t^2-11t+30=0\\\\t_1=5\; ,\; t_2=6\; \; (teorema\; Vieta)\\\\x^2=5\; ,\; \; x=\pm \sqrt5\\\\x^2=6\; ,\; \; x=\pm \sqrt6\\\\Otvet:\; \; -\sqrt6,\; -\sqrt5\; ,\; \sqrt5\; ,\; \sqrt6\; .[/latex] [latex]2)\; \; x(x+1)-(x+2)(x+3)+8=x(x+4)-(x+5)(x+2)\\\\x^2+x-x^2-5x-6+8=x^2+4x-x^2-7x-10\\\\-4x+2=-3x-10\\\\x=12[/latex]