Question

Помогите пожалуйста номер 176

Answer 1

$1) frac{ x^{2} +14x+24}{x-2} =0 \ left { {{x^{2} +14x+24=0} atop {x-2 neq 0}} \ right. \ left { {{x^{2} +14x+24=0} atop {x neq 2}} \ right. \ x^{2} +14x+24=0 \ x_{1}+x_{1}=-14 \ x_{1} x_{2}=24 \ \ x_{1}=-12 \ x_{2}=-2 \ x neq 2$

$2) frac{ x^{2} +12x-13}{x-1}=0 \ left { {{x^{2} +12x-13=0} atop {x-1 neq 0}} right. \ left { {{x^{2} +12x-13=0} atop {x neq 1}} right. \ x^{2} +12x-13=0 \ \ x_{1}+x_{1}=-12 \ x_{1} x_{2}=-13 \ \ x_{1}=-13 \ x_{2}=1 \ x neq 1 \ \ x=-13$

$3) frac{ 3x^{2}-4x-20 }{x+4} =0 \ left { {{3x^{2}-4x-20=0} atop {x+4} neq 0}} right. \ left { {{3x^{2}-4x-20=0} atop {x} neq -4}} right. \ \ D=(-4)^{2}-4*(-20)*3=16+240=256 \ x_{1}= frac{-(-4)- sqrt{256} }{2*3} = frac{4-16}{6} = frac{-12}{6} =-2 \ x_{2}= frac{-(-4)+ sqrt{256} }{2*3} = frac{4+16}{6} = frac{20}{6} =3 frac{2}{6}=3 frac{1}{3} \ \ x_{1}=-2 \ x_{2}=3 frac{1}{3} \ x neq -4$

$4) frac{6 x^{2} -5x-4}{5-x} =0 \ left { {{6 x^{2} -5x-4=0} atop {5-x neq 0}} right. \ left { {{6 x^{2} -5x-4=0} atop {x neq 5}} right. \ 6 x^{2} -5x-4=0 \ \ D=(-5)^{2}-4*(-4)*6=25+96=121 \ x_{1}= frac{-(-5)+ sqrt{121} }{2*6} = frac{5+11}{12} = frac{16}{12}= frac{4}{3}=1 frac{1}{3} \ x_{2}= frac{-(-5)- sqrt{121} }{2*6} = frac{-6}{12} = - 0.5 \ \ x_{1}=1 frac{1}{3} \ x_{2}=-0,5 \ x neq 5$