#7-Найдите корни уравнения: a)[tex] \frac{x^2}{4} =2x-3[/tex] [tex]b) \frac{x^2}{3} =5x-12 [/tex] [tex]v) \frac{x^2+1}{5} =2x-4[/tex] [tex]g) \frac{x^2-1}{2} =6x-18[/tex] [tex]d) x^2-6 = \frac{8x-9}{5} [/tex] [tex]e) x^2-5 = \frac{5x+2}{4}[/tex] [tex]h) \frac{7x+5}{4} = \frac{x^2+x}{3} [/tex] [tex]z) \frac{x^2-x}{5} = \frac{3x+1}{4} [/tex]. Created by DHAcity. algebra-ru

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$a) x^{2} =4*(2x-3) \\ \\ x^{2} =8x-12 \\ \\ x^{2} -8x+12=0 \\ \\ D=8^2-4*12=16=4^2 \\ \\ x_1= \frac{8-4}{2}=2 \\ \\ x_2= \frac{8+4}{2}=6 \\$

$b) x^{2} =3(5x-12) \\ \\ x^{2} =15x-36 \\ \\ x^{2} -15x+36=0 \\ \\ D=15^2-4*36=81=9^2 \\ \\ x_1= \frac{15-9}{2}=3 \\ \\ x_2= \frac{15+9}{2}=12$

$v) x^{2} +1=5(2x-4) \\ \\ x^{2} +1=10x-20 \\ \\ x^{2} -10x+1+20=0 \\ \\ x^{2} -10x+21=0 \\ \\ D=10^2-4*21=16=4^2 \\ \\ x_1= \frac{10-4}{2}=3 \\ \\ x_2= \frac{10+4}{2}=7$

$g) x^{2} -1=2(6x-18) \\ \\ x^{2} -1=12x-36 \\ \\ x^{2} -12x-1+36=0 \\ \\ x^{2} -12x+35=0 \\ \\ D=12^2-4*35=4=2^2 \\ \\ x_1= \frac{12-2}{2}=5 \\ \\ x_2=\frac{12+2}{2}=7 \\$

$d) 5( x^{2} -6)=8x-9 \\ \\ 5 x^{2} -30=8x-9 \\ \\ 5 x^{2} -8x-21=0 \\ \\ D=8^2+4*5*21=484=22^2 \\ \\ x_1= \frac{8-22}{2*5}=-1.4 \\ \\ x_2= \frac{8+22}{2*5}= \frac{30}{10}=3$

$e) 4( x^{2} -5)=5x+2 \\ \\ 4 x^{2} -20-5x-2=0 \\ \\ 4 x^{2} -5x-22=0 \\ \\ D=5^2+4*4*22=377 \\ \\ x_1= \frac{5- \sqrt{377} }{8} \\ \\ x_2= \frac{5+ \sqrt{377} }{8}$

$h)3(7x+5)=4( x^{2} +x) \\ \\ 21x+15=4 x^{2} +4x \\ \\ 4 x^{2} +4x-21x-15=0 \\ \\ 4 x^{2} -17x+15=0 \\ \\ D=17^2+4*4*15=529=23^2 \\ \\ x_1= \frac{17-23}{8} =-0.75 \\ \\ x_2= \frac{17+23}{8}=5 \\$

$z)4( x^{2} -x)=5(3x+1) \\ \\ 4 x^{2} -4x=15x+5 \\ \\ 4 x^{2} -4x-15x-5=0 \\ \\ 4 x^{2} -19x-5=0 \\ \\ D=19^2+4*4*5=441=21^2 \\ \\ x_1= \frac{19-21}{2*4}=-0.25 \\ \\ x_2= \frac{19+21}{2*4}=5$

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