Question

Решите уравнения через дискриминант (х+2)(-х+6)=0
х в квадрате+18=9х
2х в квадрате-3х+1=0
2х в квадрате+5х-7=0

Answer 1

$\displaystyle (x+2)(-x+6)=0\\-x^2-2x+6x+12=0\\x^2-4x-12=0\\D=(-4)^2-4\times(-12)=16+48=64\\\\x_1=\frac{4+\sqrt{64} }{2} =\frac{4+8}{2} =2+4=6\\\\x_2=\frac{4-\sqrt{64} }{2} =\frac{4-8}{2} =2-4=-2$

$\displaystyle x^2+18=9x\\x^2-9x+18=0\\D=(-9)^2-4\times 18=81-72=9\\\\x_1=\frac{9+\sqrt{9} }{2} =\frac{9+3}{2} =4,5+1,5=6\\\\x_2=\frac{9-\sqrt{9} }{2} =\frac{9-3}{2} =4,5-1,5=3$

$\displaystyle 2x^2-3x+1=0\\D=(-3)^2-4\times2=9-8=1\\\\x_1=\frac{3+\sqrt{1} }{2\times2} =\frac{4}{4} =1\\\\x_2=\frac{3-\sqrt{1} }{2\times2} =\frac{2}{4} =0,5$

$\displaystyle 2x^2+5x-7=0\\D=5^2-4\times2\times(-7)=25+56=81\\\\x_1=\frac{-5+\sqrt{81} }{2\times2} =\frac{-5+9}{4} =\frac{4}{4} =1\\\\x_2=\frac{-5-\sqrt{81} }{2\times2} =\frac{-5-9}{4} =-\frac{14}{4} =-3,5$