Question

Очень срочно надо решить!!! Пожалуйста!!

Answer 1

$\boxed {\; x^2\pm px=\Big (x\pm \frac{p}{2}\Big )^2-\Big (\frac{p}{2}\Big )^2\; }\\\\\\1)\; \; 2x^2-12x+10=2(x^2-6x)+10=2\Big ((x-3)^2-9\Big )+10=2(x-3)^2-8\\\\2)\; \; -2x^2+5x+7=-2(x^2-5x)+7=-2\Big ((x-\frac{5}{2})^2-\frac{25}{4}\Big )+7=\\\\=-2(x-2,5)^2+\frac{25}{2}+7=19,5-2(x-2,5)^2\\\\3)\; \; 5x^2-8x+3=5(x^2-\frac{8}{5}x)+3=5\Big ((x-\frac{4}{5})^2-\frac{16}{25}\Big )+3=\\\\=5(x-0,8)^2-\frac{16}{5}+3=5(x-0,8)^2-0,2\\\\4)\; \; 9x^2+6x+1=(3x)^2+2\cdot 3x\cdot 1+1^2=(3x+1)^2$

$5)\; \; 2x^2-6x+5=2(x^2-3x)+5=2\Big ((x-\frac{3}{2})^2-\frac{9}{4}\Big )+5=\\\\=2(x-\frac{3}{2})^2-\frac{9}{2}+5=2(x-1,5)^2+0,5\\\\6)\; \; -2x^2+5x-3=-2(x^2-\frac{5}{2}x)-3=-2\Big ((x-\frac{5}{4})^2-\frac{25}{16}\Big )-3=\\\\=-2(x-1,25)^2+\frac{25}{8}-3=\frac{1}{8}-2(x-1,25)^2\\\\7)\; \; 4x^2-7x+3=4(x^2-\frac{7}{4}x)+3=4\Big ((x-\frac{7}{8})^2-\frac{49}{64}\Big )+3=\\\\=4(x-\frac{7}{8})^2-\frac{49}{16}+3=4(x-\frac{7}{8})^2-\frac{1}{16}$

$8)\; \; \frac{2x^2-3x-2}{x^2+3x-10}=\frac{2(x+0,5)(x-2)}{(x-2)(x+5)}=\frac{2x+1}{x+5}$