Question

Помогите пожалуйста, у меня не получается :(("
100 балов даю!!!​

Answer 1

$1a)6x^{2}-4x+32=0\\\\D=(-4)^{2}-4*6*32=16-768=-752<0$

корней нет

$1b)x^{2} +5x-6=0\\\\D=5^{2}-4*(-6)=25+24=49=7^{2}\\\\x_{1}=\frac{-5-7}{2}=-6\\\\x_{2}=\frac{-5+7}{2}=1\\\\Otvet:\boxed{-6;1}$

$2)6x^{2} +5x-20=-9\\\\6x^{2}+5x-11=0\\\\D=5^{2}-4*6*(-11)=25+264=289=17^{2}\\\\x_{1}=\frac{-5-17}{12} =-1\frac{5}{6}\\\\x_{2}=\frac{-5+17}{12}=1\\\\Otvet:\boxed{pri...x=-1\frac{5}{6}... i...x=1}$

$3)(3x-1)(x+2)=20\\\\3x^{2}+6x-x-2-20=0\\\\3x^{2}+5x-22=0\\\\D=5^{2} -4*3*(-22)=25+264=289=17^{2}\\\\x_{1}=\frac{-5-17}{6}=-3\frac{2}{3}\\\\x_{2}=\frac{-5+17}{6}=2\\\\Otvet:\boxed{-3\frac{2}{3};2}$

$4)(x+5)^{2}+(x-2)^{2}+(x-7)(x+7)=11x+80\\\\x^{2}+10x+25+x^{2}-4x+4+x^{2}-49-11x-80=0\\\\3x^{2}-5x-100=0\\\\D=(-5)^{2}-4*3*(-100)=25+1200=1225=35^{2}\\\\x_{1}=\frac{5-35}{6}=-5 \\\\x_{2}=\frac{5+35}{6}=6\frac{2}{3}\\\\Otvet:\boxed{-5;6\frac{2}{3}}$