Question

Пожалуйста помогите

Answer 1

$1)\; \; x^2-2x-8=0\\\\(x-1)^2-9=0\; \; ,\; \; (x-1-3)(x-1+3)=0\; ,\\\\(x-4)(x+2)=0\; \; ,\; \; x_1=4\; ,\; x_2=-2\\\\\\2)\; \; 2x^2-7x+5=0\; \; ,\; \; 2\cdot (x^2-\frac{7}{2}x+\frac{5}{2})=0\; ,\\\\2\cdoy \Big ((x-\frac{7}{4})^2-\frac{49}{16}+\frac{5}{2}\Big )=0\; \; ,\; \; (x-\frac{7}{4})^2-\frac{9}{16}=0\; ,\\\\(x-\frac{7}{4}-\frac{3}{4})(x-\frac{7}{4}+\frac{3}{4})=0\; \; ,\; \; \; (x-\frac{10}{4})(x-1)=0\; ,\\\\x_1=2,5\; \; ,\; \; x_2=1$

$3)\; \; -x^2-4x-7=0\; \; ,\; \; \; x^2+4x+7=0\; ,\\\\(x+2)^2-4-7=0\; \; ,\; \; \; (x+2)^2-11=0\; ,\\\\(x+2-\sqrt{11})(x+2+\sqrt{11})=0\; ,\\\\x_1=-2+\sqrt{11}\; \; ,\; \; \; x_2=-2-\sqrt{11}\\\\\\4)\; \; 3x^2-2x-3=0\; \; \; ,\; \; \; 3\cdot (x^2-\frac{2}{3}x-1)=0\; ,\\\\(x-\frac{1}{3})^2-\frac{1}{9}-1=0\; \; ,\; \; \; (x-\frac{1}{3})^2-\frac{10}{9}=0\; ,\\\\(x-\frac{1}{3}-\frac{\sqrt{10}}{3})(x-\frac{1}{3}+\frac{\sqrt{10}}{3})=0\\\\x_1=\frac{1}{3}+\frac{\sqrt{10}}{3}\; \; ,\; \; x_2=\frac{1}{3}-\frac{\sqrt{10}}{3}$

$\star \; \; \; x^2\pm px+q=(x\pm \frac{p}{2})^2-(\frac{p}{2})^2+q=(x\pm \frac{p}{2})^2-\frac{p^2}{4}+q\; \; \star$