Решение №12603: \( a=a, b=-(1-2a) c=1-3a a+b+c=0, a+(-(1-2a))+(1-3a)=a-1+2a+1-3a=0 \Rightarrow x_{1}=1 x_{1}+x_{2}=-\frac{b}{a}=\frac{1-2a}{a} -1+x_{2}=\frac{1-2a}{a} 1+x_{2}=\frac{1-2a}{a} a(a+x_{2})=1-2a a+ax_{2}=1-2a 1+x_{2}=\frac{1-2a}{a} x_{2}=\frac{1-2a-a}{a}; x_{2}=\frac{1-3a}{a} \).

Ответ: NaN

Решение №12609: \( x_{1}+x_{2}=s; x_{1}*x_{2}=m x_{1}^{2}+2x_{1}x_{2}+x_{2}^{2}=(x_{1}+x_{2})^{2}=s^{2} \).

Ответ: NaN

Решение №12613: \( x_{1}+x_{2}=s; x_{1}*x_{2}=m \left | \frac{x_{1}}{x_{2}}-\frac{x_{2}}{x_{1}} \right |=\left | \frac{x_{1}^{2}-x_{2}^{2}}{x_{1}*x_{2}} \right |=\left | \frac{(x_{1}-x_{2})(x_{1}+x_{2})}{x_{1}*x_{2}} \right |=\left | \frac{x_{1}^{2}+2x_{1}*x_{2}+x_{2}^{2}-2x_{1}*x_{2}-2x_{2}^{2}}{x_{1}*x_{2}} \right |=\left | \frac{(x_{1}+x_{2})^{2}-2x_{2}(x_{1}+x_{2})}{x_{1}*x_{2}} \right |=\left | \frac{s^{2}-2x_{2}(s)}{m} \right | \).

Ответ: NaN

Решение №12616: \( x_{1}+x_{2}=s; x_{1}*x_{2}=m (x_{1}-x_{2})^{2}=x_{1}^{2}+2x_{1}*x_{2}+x_{2}^{2}-4x_{1}*x_{2}=(x_{1}+x_{2})^{2}-4x_{1}*x_{2}=s^{2}-4m \).

Ответ: NaN

Решение №12618: \( a=1; b=-9, c=-17 x_{1}^{2}+x_{2}^{2}=x_{1}^{2}+2x_{1}*x_{2}+x_{2}^{2}-2x_{1}*x_{2}=(x_{1}+x_{2})^{2}-2x_{1}*x_{2}=9^{2}-2*(-17)=81+34=115 x_{1}+x_{2}=9 x_{1}*x_{2}=-17 \).

Ответ: NaN

Решение №12620: \( a=3; b=8; c=-1 x_{1}+x_{2}=-\frac{b}{a}=\frac{-8}{3}; x_{1}*x_{2}=\frac{c}{a}=-\frac{1}{3} x_{1}^{2}+x_{2}^{2}=x_{1}^{2}+2x_{1}*x_{2}+x_{2}^{2}-2x_{1}*x_{2}=(x_{1}+x_{2})^{2}-2x_{1}*x_{2}=(-\frac{8}{3})^{2}-2*(-\frac{1}{3})=\frac{64}{9}+\frac{2}{3}=\frac{64}{9}+\frac{6}{9}=\frac{70}{9} \).

Ответ: NaN

Решение №12621: \( a=3; b=8; c=-1 x_{1}+x_{2}=-\frac{b}{a}=\frac{-8}{3}; x_{1}*x_{2}=\frac{c}{a}=-\frac{1}{3} x_{1}^{2}*x_{2}+4x_{2}^{2}=x_{1}*x_{2}(x_{1}+x_{2})=-\frac{1}{3}*(-\frac{8}{3})=\frac{8}{9} \).

Ответ: NaN

Решение №12622: \( x_{1}\) и \( x_{2}\) - корни уравнения. \( a=1; b=-5; c=-11 x_{1}+x_{2}=-5 x_{1}*x_{2}=-11 \frac{x_{1}}{x_{2}}+\frac{x_{2}}{x_{1}}+6=\frac{x_{1}^{2}+x_{2}^{2}}{x_{1}*x_{2}}+6=\frac{x_{1}^{2}-2*(-11)-2x_{1}*x_{2}}{x_{1}*x_{2}}+6=\frac{(x_{1}+x_{2})^{2}-2x_{1}*x_{2}}{x_{1}*x_{2}}+6=\frac{5^{2}+-2*(-11)}{-11}+6=\frac{25+22}{-11}+6=\frac{47}{-11}+6-\frac{47}{11}+6=-\frac{47}{11}+\frac{66}{11}=\frac{66-47}{11}=\frac{19}{11} \).

Ответ: NaN

Решение №12628: \( x_{1}\) и \( x_{2}\) - корни уравнения. \( a=2p; b=(p^{2}-9); c=-5p+2 x_{1}+x_{2}=-\frac{b}{a} x_{1}+x_{2}=-\frac{p^{2}-9}{2p} -x_{2}+x_{2}=-\frac{p^{2}-9}{2p} 0=-\frac{p^{2}-9}{2p} p^{2}-9=0 p=\pm \sqrt{9} p=\pm 3 p=3; 2*3x^{2}+(3^{2}-9)x-5*3+2=0 6x^{2}-13=0 6x^{2}=13 x^{2}=\frac{13}{6} x=\pm \sqrt{\frac{13}{6}} p=-3; 2*(-3)x^{2}+((-3)^{2}-9)x-5*(-3)+2=0 -6x^{2}+17=0 -6x^{2}=-17 x^{2}=\frac{17}{6} x=\pm \sqrt{\frac{17}{6}} \).

Ответ: NaN

Решение №12629: \( x_{1}\) и \( x_{2}\) - корни уравнения. \( x_{1}=2p; b=5; c=p+1 x_{1}*x_{2}=\frac{a}{c} \frac{1}{x_{2}}*x_{2}=\frac{p+1}{2p} 1=\frac{p+1}{2p} 2p=p+1 2p-p=1 p=1 2*1x^{2}+5x+1+1=0 2x^{2}+5x+2=0 D=5^{2}-4*2*2=25-16=9 x_{1}=\frac{-5-3}{4}=-2; x_{2}=\frac{-5+3}{4}=-\frac{1}{2} \).

Ответ: NaN

Решение №12630: \( x_{1}\) и \( x_{2}\) - корни уравнения. \( x_{1}^{2}+x_{2}^{2}=65 a=1; b=3p-5; c=3p^{2}-11-6 (x_{1}+x_{2})^{2}-2x_{1}x_{2}=65 (-(3p-5))^{2}-2(3p^{2}-11p-6)=65 9p^{2}-30p+25-6p^{2}+22p+12-65=0 3p^{2}-8p-28=0 D=64-4*3*(-28)=64+336=400=20^{2} p_{1}=\frac{8-20}{6}=2; p_{2}=\frac{28}{6}=\frac{14}{3} p=-2; x^{2}-11x+28=0 D=121-112=9=3^{2} x_{1}=\frac{11-3}{2}=4; x_{2}=7 p=\frac{14}{3}; x^{2}+(3*\frac{14}{3}-5)x+(3*\frac{196}{9}-11\frac{14}{3}-6)=0 x^{2}+9x+\frac{196}{3}-\frac{154}{3}-6=0 x^{2}+9x+9=0 D=81-4*1*8=7^{2} x_{1}=-8; x_{2}=-1 \).

Ответ: NaN

Решение №12631: \( x_{1}\) и \( x_{2}\) - корни уравнения. \( x_{1}-x_{2}=2,5 a=2; b=-15; c=p x_{1}+x_{2}=-\frac{b}{a} x_{1}+x_{2}=\frac{15}{2} 2,5+x_{2}+x_{2}=7,5 2x_{2}=7,5-2,5 2x_{2}=5 x_{2}=2,5 x_{1}*x_{2}=\frac{c}{a} x_{1}*x_{2}=\frac{p}{2} x_{1}=2,5+2,5 x_{1}=5 x_{1}=2,5+x_{2} x_{1}*x_{2}=\frac{p}{2} 2,5*5=\frac{p}{2} 12,5=\frac{p}{2} p=12,5*2 p=25 \).

Ответ: NaN

Решение №12632: \( x_{1}\) и \( x_{2}\) - корни уравнения. \( x_{1}=2,5x_{2} a=2; b=-14; c=p x_{1}+x_{2}=-\frac{b}{a} x_{1}+x_{2}=\frac{14}{2} x_{1}+x_{2}=7 2,5x_{2}+x_{2}=7 3,5x_{2}=7 x_{2}=2 x_{1}=2,5*2=5 x_{1}*x_{2}=\frac{c}{a} x_{1}*x_{2}=\frac{p}{2} 2*5=\frac{p}{2} 10=\frac{p}{2} p=10*2 p=20 \).

Ответ: NaN

Решение №12634: \( m\) и \( n\) - корни уравнения. \( x^{2}-px+q=0 a=1; b=-p; c=a \left\{\begin{matrix}x_{1}+x_{2}=p \\ x_{1}*x_{2}=q \end{matrix}\right.\Rightarrow \left\{\begin{matrix}m+n=p \\ m*n=q \end{matrix}\right.\Rightarrow \left\{\begin{matrix}x+y=p \\ xy=q \end{matrix}\right. \).

Ответ: NaN

Решение №12635: \( \left\{\begin{matrix}x=-7-y \\ (-7-y)y=12 \end{matrix}\right. \left\{\begin{matrix}x_{1}=-7-(-3) \\ y_{1}=-3 \end{matrix}\right. \left\{\begin{matrix}x_{1}=-4 \\ y_{1}=-3 \end{matrix}\right. \left\{\begin{matrix}y_{2}=-4 \\ x_{2}=-3 \end{matrix}\right. -7y-y^{2}-12=0 | *(-1) y^{2}+7y+12=0 D=7^{2}-4*12=49-48=1 y_{1}=\frac{-7+1}{2}=-3; y_{2}=\frac{-7-1}{2}=-4 \).

Ответ: NaN

Решение №12638: \( \left\{\begin{matrix}2x+7y=4 \\ 14xy=3 \end{matrix}\right. \left\{\begin{matrix}2x=4-7y \\ 14xy=3 \end{matrix}\right. \left\{\begin{matrix}x=\frac{4-7y}{2} \\ 14*\frac{4-7y}{2}*y=3 \end{matrix}\right. 7(4-7y)y=3 28y-49y^{2}-3=0 -49y^{2}+28y-3=0 | *(-1) 49y^{2}-28y+3=0 D=(-28)^{2}-4*49*3=784-588=196=14^{2} y_{1}=\frac{28-14}{2*49}=\frac{14}{2*49}=\frac{2*7}{2*7*7}=\frac{1}{7} y_{2}=\frac{28+14}{2*49}=\frac{42}{2*49}=\frac{3}{7} x_{1}=\frac{4-7*\frac{1}{7}}{2}=\frac{4-1}{2}=\frac{3}{2} x_{2}=\frac{4-7*\frac{3}{7}}{2}=\frac{4-3}{2}=\frac{1}{2} \).

Ответ: NaN

Решение №12642: \( \left\{\begin{matrix}2x+2y+xy=8 \\3x+3y-xy=7 \end{matrix}\right. \left\{\begin{matrix}5x+5y=15 \\ 3x+3y-xy=7 \end{matrix}\right. \left\{\begin{matrix}x+y=3 \\ 3x+3y-xy=7 \end{matrix}\right. \left\{\begin{matrix}x=3-y \\ 3(3-y)+3y-(3-y)y=7 \end{matrix}\right. 9-3y+3y-3y+y^{2}=7 y^{2}-3y+9-7=0 y^{2}-3y+2=0 D=(-3)^{2}-4*1*2=9-8=1 y_{1}=\frac{3-1}{2}=1; y_{2}=\frac{3+1}{2}=2 x_{1}=3-1=2 x_{2}=3-2=1 \).

Ответ: NaN

Решение №12651: \( x^{2}+3x-10=0 D=3^{2}-4*1*(-10)=9+40=49=7^{2} x_{1}=\frac{-3-7}{2}=\frac{-10}{2}=-5 x_{2}=\frac{-3+7}{2}=2 x^{2}+3x-10=(x+5)(x-2) \).

Ответ: NaN

Решение №12653: \( -x^{2}-8x+9=0 | *(-1) x^{2}+8x-9=0 D=8^{2}-4*1*(-9)=64+36=100=10^{2} x_{1}=\frac{-8-10}{2}=-9 x_{2}\frac{-8+10}{2}=1 -x^{2}-8x+9=(x+9)(x-1) \).

Ответ: NaN

Решение №12655: \( -x^{2}+7x+8=0 D=7^{2}*(-1)*8=49+32=81=9^{2} x_{1}=\frac{-7-9}{-2}=8 x_{2}=\frac{-7+9}{-2}=-1 -x^{2}+7x+8=-(x-8)(x+1) \).

Ответ: NaN

Решение №12656: \( 3x^{2}+5x-2=0 D=5^{2}-4*3*(-2)=25+24=49=7^{2} x_{1}=\frac{-5-7}{6}=\frac{-12}{6}=-2 x_{2}=\frac{-5+7}{6}=\frac{2}{6}=\frac{1}{3} 3x^{2}+5x-2=(x+2)(x-\frac{1}{3})=(x+2)(3x-1) \).

Ответ: NaN

Решение №12658: \( 5x^{2}+2x-3=0 D=2^{2}-4*5*(-3)=4+60=64=8^{2} x_{1}=\frac{-2-8}{10}=-1 x_{2}=\frac{-2+8}{10}=\frac{6}{10}=\frac{3}{5} 5x^{2}+2x-3=(x+1)(x-\frac{3}{5})=(5x-3)(x+1) \).

Ответ: NaN

Решение №12659: \( 15x^{2}-8x+1=0 D=(-8)^{2}-4*15*1=64-60=4=2^{2} x_{1}=\frac{8-2}{30}=\frac{6}{30}=\frac{1}{5} x_{2}=\frac{8+2}{30}=\frac{1}{3} 15x^{2}-8x+1=(x-\frac{1}{5})(x-\frac{1}{3})=(5x-1)(3x-1) \).

Ответ: NaN

Решение №12664: \( x^{2}-12x+24=0 D=(-12)^{2}-4*1*24=144-96=48 x_{1}=\frac{12-\sqrt{48}}{2}=\frac{12-\sqrt{16*3}}{2}=\frac{12-4\sqrt{3}}{2}=6-2\sqrt{3} x_{2}=\frac{12+\sqrt{48}}{2}=6+2\sqrt{3} x^{2}-12x+24=(x-6+2\sqrt{3})(x-6-2\sqrt{3}) \).

Ответ: NaN

Решение №12676: \( \sqrt{x}=y 7y^{2}+23y+16=0 D=23^{2}-4*7*16=529-448=81=9^{2} y_{1}=\frac{-23-9}{14}=\frac{-32}{14}=-\frac{16}{7}=-2\frac{2}{7} y_{2}=\frac{-23+9}{14}=-\frac{14}{14}=-1 7x+23\sqrt{x}+16=7(\sqrt{x}+2\frac{2}{7})(\sqrt{x}+1)=(\sqrt{x}+1)(7\sqrt{x}+16) \).

Ответ: NaN

Решение №12679: \( \sqrt{x}=y 2y^{2}-5y+2=0 D=(-5)^{2}-4*2*2=25-16=9=3^{2} y_{1}=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2} y_{2}=\frac{5+3}{4}=\frac{8}{4}=2 2x^{3}-5x\sqrt{x}+2=2(x\sqrt{x}-2)(x\sqrt{x}-\frac{1}{2})=(x\sqrt{x}-2)(2x\sqrt{x}-1) \).

Ответ: NaN

Решение №12681: \( x^{3}=y -2y^{2}+9y-4=0 D=9^{2}-4*(-2)*(-4)=81-32=49=7^{2} y_{1}=\frac{-9-7}{-2*2}=\frac{-16}{-4}=4 y_{2}=\frac{-9+7}{-4}=\frac{-2}{-4}=\frac{1}{2} -2x^{6}+9x^{3}-4=-(x^{3}-4)(x^{3}-\frac{1}{2})=(x^{3}-4)(2x^{3}-1)=(4-x^{3})(2x^{3}-1) \).

Ответ: NaN

Решение №12683: \( x^{3}=y 15y^{2}-8y+1=0 D=(-8)^{2}-4*15*1=64-60=4=2^{2} y_{1}=\frac{8-2}{30}=\frac{6}{30}=\frac{1}{5} y_{2}=\frac{8+2}{30}=\frac{10}{30}=\frac{1}{3} 15x^{6}-8x^{3}+1=(x^{3}-\frac{1}{5})(x^{3}-\frac{1}{3})=(5x^{3}-1)(3x^{3}-1) \).

Ответ: NaN

Решение №12685: \( \frac{3x^{2}+10x+3}{x^{2}-3x}=\frac{(3x-1)(x-3)}{x(x-3)}=\frac{3x-1}{x} 3x^{2}-10x+3=0 D=(-10)^{2}-4*3*3=100-36=64=8^{2} x_{1}=\frac{10-8}{2*3}=\frac{1}{3} x_{2}=\frac{10+8}{6}=3 3x^{2}-10x+3=3(x-\frac{1}{3})(x-3)=(3x-1)(x-3) \).

Ответ: \frac{3x-1}{x}

Решение №12687: \( \frac{5x^{2}+x-4}{x^{2}+x}=\frac{(x+1)(5x-4)}{x(x+1)}=\frac{5x-4}{x} 5x^{2}+x-4=0 D=1^{2}-4*5*(-4)=1+80=81=9^{2} x_{1}=\frac{-1-9}{2*5}=\frac{-10}{10}=-1 x_{2}=\frac{-1+9}{2*5}=\frac{8}{10}=\frac{4}{5} 5x^{2}+x=5(x+1)(x-\frac{4}{5})=(x+1)(5x-4) \).

Ответ: \frac{5x-4}{x}