Question

#7-Найдите корни уравнения:

a)$frac{x^2}{4} =2x-3$

$b) frac{x^2}{3} =5x-12$

$v) frac{x^2+1}{5} =2x-4$

$g) frac{x^2-1}{2} =6x-18$

$d) x^2-6 = frac{8x-9}{5}$

$e) x^2-5 = frac{5x+2}{4}$

$h) frac{7x+5}{4} = frac{x^2+x}{3}$

$z) frac{x^2-x}{5} = frac{3x+1}{4}$

Answer 1

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

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

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

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

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

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

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

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

Answer 2

Е) Д неверно найден.