Question

Решите объведённые номера.

Answer 1

$1)\ 10x-5x^2=0\ (:5)\\2x-x^2=0\\x(2-x)=0\\x_1=0\\or\\2-x=0\\-x=-2\\x_2=2.$

$2)\ x^2-10x+9=0\\D=(-10)^2-4\cdot1\cdot9=100-36=64\\\\x_{1/2}=\displaystyle \frac{10\pm8}{2}\\\\x_1=\frac{10-8}{2}=\frac{2}{2}=1\\\\x_2=\frac{10+8}{2}=\frac{18}{2}=9.$

$3)\ 7x^2+9x+2=0\\D=9^2-4\cdot7\cdot2=81-56=25\\\\x_{1/2}=\displaystyle\frac{-9\pm5}{14}\\\\x_1=\frac{-9-5}{14}=\frac{-14}{14}=-1\\\\x_2=\frac{-9+5}{14}=\frac{-4}{14}=-\frac{2}{7}.$

Answer 2

$1)\\10x-5x^2=0\\2x-x^2=0\\x(2-x)=0\\\\x=0\\2-x=0\\x=2\\x={0;2}$

$2)\\x^2-10x+9=0\\a=1,b=-10,c=9\\D=b^2-4*a*c=(-10)^2-4*1*9=100-36=64\\x=\frac{10-\sqrt{64} }{2*1} =\frac{10-8}{2} =\frac{2}{2} =1\\x=\frac{10+\sqrt{64} }{2*1} =\frac{10+8}{2} =\frac{18}{2} =9\\x={1;9}$$3)\\7x^2+9x+2=0\\a=7,b=9,c=2\\D=b^2-4*a*c=9^2-4*7*2=81-56=25\\x=\frac{-9-\sqrt{25} }{2*7} =\frac{-9-5}{14} =\frac{-14}{14} =-1\\x=\frac{-9+\sqrt{25} }{2*7} =\frac{-9+5}{14} =\frac{-4}{14} =\frac{-2}{7} \\x={-1;-2/7}$