Решение №6320: \( x_{1}+x_{2}=s; x_{1}*x_{2}=m x_{1}^{2}-2x_{1}x_{2}+x_{2}^{2}=x_{1}^{2}+2x_{1}*x_{2}+x_{2}^{2}-4x_{1}*x_{2}=(x_{1}+x_{2})^{2}-4x_{1}*x_{2}=s^{2}-4m \).

Ответ: NaN

Решение №6321: \( x_{1}+x_{2}=s; x_{1}*x_{2}=m \frac{x_{1}x_{2}}{x_{1}+x_{2}}=\frac{m}{s} \).

Ответ: NaN

Решение №6325: \( a=1; b=-9, c=-17 x_{1}^{2}x_{2}+x_{1}*x_{2}^{2}=x_{1}*x_{2}(x_{1}+x_{2})=-17*9=-153 \).

Ответ: NaN

Решение №6331: \( x_{1}\) и \( x_{2}\) - корни уравнения. \( a=3; b=-5; c=-4 x_{1}+x_{2}=-\frac{b}{a}=\frac{5}{3} x_{1}*x_{2}=\frac{c}{a}=-\frac{4}{3} \frac{x_{2}(6+5x_{1})+x_{1}(6-7x_{2})}{x_{1}*x_{2}}=\frac{6x_{2}+5x_{1}*x_{2}+6x_{1}-7x_{1}*x_{2}}{x_{1}*x_{2}}=\frac{6(x_{1}+x_{2})-2x_{1}*x_{2}}{x_{1}*x_{2}}=\frac{6*\frac{5}{3}-2*(-\frac{4}{3})}{-\frac{4}{3}}=\frac{10+\frac{8}{3}}{-\frac{4}{3}}=\frac{12\frac{2}{3}}{-\frac{4}{3}}=\frac{38}{3}*(-\frac{3}{4})=-\frac{38}{4}=-9,5 \).

Ответ: NaN

Решение №6333: \( x_{1}\) и \( x_{2}\) - корни уравнения. \( x_{1}*x_{2}=-21 p=?; x_{1}=?; x_{2}=? a=1; b=-(p+1); c=2p^{2}-9p-12 x_{1}*x_{2}=c 2p^{2}-9p-12=-21 2p^{2}-9p-12+21=0 2p^{2}-9p+9=0 D=(-9)^{2}-4*2*9=81-72=9=3^{2} p_{1}=\frac{9-3}{4}=\frac{6}{4}=\frac{3}{2}; p_{2}=\frac{9+3}{4}=\frac{12}{4}=3 p=\frac{3}{2}=1,5 x^{2}-(1,5+1)x+(2*1,5^{2}-9*1,5-12)=0 x^{2}-2,5x+(2*2,25-13,5-12)=0 x^{2}-2,5x+(4,5-25,5)=0 x^{2}-2,5x-21=0 2x^{2}-5x-42=0 D=(-5)^{2}-4*2*(-42)=25+336=361=192 x_{1}=\frac{5-19}{4}=\frac{-14}{4}=-\frac{7}{2}; x_{2}=\frac{5+19}{4}=\frac{24}{4}=6 p=3 x^{2}-(3+1)x+(2*3^{2}-9*3-12)=0 x^{2}-4x+(2*9-27-12)=0 x^{2}-4x+(18-39)=0 x^{2}-4x-21=0 D=(-4)^{2}-4*1*(-8)=16+82=98> 0 \).

Ответ: NaN

Решение №6346: \( \left\{\begin{matrix}x+y-xy=-13 \\ x+y+xy=35 \end{matrix}\right. \left\{\begin{matrix}2x+2y=22 | : 2 \\ x+y+xy=35 \end{matrix}\right. \left\{\begin{matrix}x+y=11 \\ x+y+xy=35 \end{matrix}\right. \left\{\begin{matrix}x=11-y \\ 11-y+y+(11-y)*y=35 \end{matrix}\right. 11+11y-y^{2}-35=0 -y^{2}+11y-24=0 | *(-1) y^{2}-11y+24=0 D=(-11)^{2}-4*1*24=121-96=25=5^{2} y_{1}=\frac{11-5}{2}=\frac{6}{2}=3; y_{2}=\frac{11+5}{2}=\frac{16}{2}=8 x_{1}=11-3=8; x_{2}=11-8=3 \).

Ответ: NaN

Решение №6350: \( 2x^{2}+3x+1=0 D=3^{2}-4*2*1=9-8=1 x_{1}=\frac{-3-1}{4}=-1; x_{2}=\frac{-3+1}{4}=-\frac{1}{2} 2x^{2}+3x+1=(x+1)(x+\frac{1}{2}) \).

Ответ: NaN

Решение №6352: \( -12x^{2}+7x+1=0 | *(-1) 12x^{2}+7x+1=0 D=7^{2}-4*12*1=49-48=1 x_{1}=\frac{-7-1}{2*12}=\frac{-8}{24}=-\frac{1}{3}; x_{2}=\frac{-7+1}{24}=\frac{-6}{24}=-\frac{1}{4} -12x^{2}-7x-1=(x+\frac{1}{3})(x+\frac{1}{4}) \).

Ответ: NaN

Решение №6355: \( x^{2}-2x-15=0 D=(-2)^{2}-4*1*(-15)=4+16=64=8^{2} x_{1}=\frac{2-8}{2}=\frac{-6}{2}=-3 x_{2}=\frac{2+8}{2}=5 x^{2}-2x-15=(x+3)(x-5) \).

Ответ: NaN

Решение №6358: \( -x^{2}+16x-15=0 | *(-1) x^{2}-16x+15=0 D=(-16)^{2}-4*1*15=256-60=196=14^{2} x_{1}=\frac{16-14}{2}=1 x_{2}=\frac{16+14}{2}=15 -x^{2}+16x-15=(x-1)(x-15) \).

Ответ: NaN

Решение №6363: \( 6x^{2}+5x+1=0 D=5^{2}-4*6*1=25-24=1 x_{1}=\frac{-5-1}{12}=\frac{-6}{12}=-\frac{1}{2}; x_{2}=\frac{-5+1}{12}=-\frac{1}{3} 6x^{2}+5x+1=(x+\frac{1}{2})(x+\frac{1}{3})=(2x+1)(3x+1) \).

Ответ: NaN

Решение №6369: \( -4x^{2}+3x-85=0 D=32-4*(-85)*4=9+1360=1369=37^{2} x_{1}=\frac{-3-37}{2*4}=-\frac{40}{8}=-5; x_{2}=\frac{-3+37}{8}=\frac{34}{8}=4,25 -4x^{2}-3x+85=4(x+5)(x-4,25)=-(4x-17)(x+5) \).

Ответ: NaN

Решение №6372: \( x^{2}-6x+1=0 D=(-6)^{2}-4*1*1=16-4=12 x_{1}=\frac{6-\sqrt{12}}{2}=\frac{6-\sqrt{4*3}}{2}=\frac{6-2\sqrt{3}}{2}=3-\sqrt{3} x_{2}=3+\sqrt{3} x^{2}-6x+1=(x-3+\sqrt{3})(x-3-\sqrt{3}) \).

Ответ: NaN

Решение №6373: \( 4x^{2}-12x+7=0 D=(-12)^{2}-4*4*7=144-112=32 x_{1}=\frac{12-\sqrt{32}}{2*4}=\frac{12-\sqrt{16*2}}{8}=\frac{12-4\sqrt{2}}{8}=\frac{4(3-\sqrt{2})}{8}=\frac{3-\sqrt{2}}{2} x_{2}=\frac{3+\sqrt{2}}{2} 4x^{2}-12x+7=(x-\frac{3-\sqrt{2}}{2})(x-\frac{3+\sqrt{2}}{2}) \).

Ответ: NaN

Решение №6377: \( -8x^{2}+40x-50=0 | :(-5) 1,6x^{2}-8x+10=0 D=(-8)^{2}-4*1*6=64-64=0 x=\frac{8}{2*1,6}=\frac{8}{3,2}=\frac{1}{0,4}=\frac{1}{\frac{4}{10}}=\frac{10}{4}=2\frac{1}{2} -8x^{2}+40x-50=(x-2,5)(x-2,5) \).

Ответ: NaN

Решение №6381: \( \sqrt{x}=y y^{2}+3y-40=0 D=3^{2}-4*1*(-40)=9+160=169=13^{2} y_{1}=\frac{-3-13}{2}=-8 y_{2}=\frac{-3+13}{2}=5 x+3\sqrt{x}-40=(\sqrt{x}+8)(\sqrt{x}-5) \).

Ответ: NaN

Решение №6383: \( \sqrt{x}=y 3y^{2}-10y+3=0 D=(-10)^{2}-4*3*3=100-36=64=8^{2} y_{1}\frac{10+8}{6}=3; y_{2}=\frac{10-8}{6}=\frac{1}{3} 3x^{3}-10x\sqrt{x}+3=3(x\sqrt{x}-3)(x\sqrt{x}-\frac{1}{3})=(x\sqrt{x}-3)(3x\sqrt{x}-1) \).

Ответ: NaN

Решение №6386: \( x^{2}=y y^{2}-13y+36=0 D=(-13)^{2}-4*1*36=196-144=25=5^{2} y_{1}=\frac{13-5}{2}=\frac{8}{2}=4 y_{2}=\frac{13+5}{2}=\frac{18}{2}=9 x^{4}-13x^{2}+36=(x^{2}-4)(x^{2}-9)=(x-2)(x+2)(x-3)(x+3) \).

Ответ: NaN

Решение №6388: \( x^{2}=y -y^{2}+20y-64=0 | *(-1) y^{2}-20y+64=0 D=(-20)^{2}-4*1*64=400-256=144=12^{2} y_{1}=\frac{20-12}{2}=\frac{8}{2}=4; y_{2}=\frac{20+12}{2}=16 -x^{4}+20x^{2}-64=(x^{2}-4)(x^{2}-16)=(x-2)(x+2)(x-4)(x+4) \).

Ответ: NaN

Решение №6396: \( \frac{2x^{2}+7x-4}{x^{2}-16}=\frac{(x+4)(2x-1)}{(x-4)(x+4)}=\frac{2x-1}{x-4} 2x^{2}+8x-4=0 D=7^{2}-4*2*(-4)=19+181=9^{2} x_{1}=\frac{-7-9}{2*2}=-\frac{16}{4}=-4 x_{2}=\frac{-7+9}{4}=\frac{1}{2} 2x^{2}+7x-4=2(x+4)(x-\frac{1}{2})=(x+4)(2x-1) \).

Ответ: NaN

Решение №6400: \( \frac{6x^{2}-19x+13}{2x^{2}+7x-9}=\frac{(x-1)(6x-13)}{(2x+9)(x-1)}=\frac{6x-13}{2x+9} 6x^{2}-19x+13=0 D=(-19)^{2}-4*6*13=361-312=49=7^{2} x_{1}=\frac{19-7}{6*2}=1 x_{2}=\frac{19+7}{12}=\frac{13}{6} 6x^{2}-19x+13=(x-1)(6x-13) 2x^{2}+7x-9=0 D=7^{2}-4*2*(-9)=49+72=121=11^{2} x_{1}=\frac{-7-11}{4}=\frac{-18}{4}=-\frac{9}{2} x_{2}=\frac{-7+11}{4}=\frac{4}{4}=1 2x^{2}+7x-9=2(x+\frac{9}{2})(x-1)=(2x+9)(x-1) \).

Ответ: NaN

Решение №6401: \( \frac{21x^{2}+x-2}{2+5x-3x^{2}}=\frac{(3x+1)(7x-2)}{-(x-2)(3x+1)}=-\frac{7x-2}{x-2}=\frac{7x-2}{2-x} 21x^{2}+x-2=0 D=1-4*21*(-2)=1+168=169=13^{2} x_{1}=\frac{-1+13}{2*21}=\frac{12}{42}=\frac{2}{7} x_{2}=\frac{-1-13}{42}=-\frac{14}{42}=-\frac{1}{3} 21x^{2}+x-2=21(x+\frac{1}{3})(x-\frac{2}{7})=(3x+1)(7x-2) 2+5x-3x^{2}=0 D=5^{2}-4*2*(-3)=25+24=49=7^{2} x_{1}=\frac{-5-7}{2*(-3)}=\frac{-12}{-6}=2 x_{2}=\frac{-5+7}{-6}=-\frac{1}{3} -3x^{2}+5x+2=-3(x-2)(x+\frac{1}{3})=-(x-2)(3x+1) \).

Ответ: NaN

Решение №6404: \( \frac{2x+11\sqrt{x}-6}{x+3\sqrt{x}-18}=\frac{(\sqrt{x}+6)(2\sqrt{x}-1)}{(\sqrt{x}+6)(\sqrt{x}-3)}=\frac{2\sqrt{x}-1}{\sqrt{x}-3} 2x+11\sqrt{x}-6=0 D=11^{2}-4*2*(-6)=121+48=169=13^{2} \sqrt{x}=\frac{-11-13}{2*2}=-6 \sqrt{x}=\frac{-11+13}{4}=\frac{1}{2} 2x+11\sqrt{x}-6=2(\sqrt{x}+6)(\sqrt{x}-\frac{1}{2}) x+3\sqrt{x}-18=0 D=3^{2}-4*1*(-18)=9+72=81=9^{2} \sqrt{x}=\frac{-3-9}{2}=-\frac{12}{2}=-6 \sqrt{x}=\frac{-3+9}{2}=3 x+3\sqrt{x}-18=(\sqrt{x}+6)(\sqrt{x}-3) \).

Ответ: NaN

Решение №6406: \( \frac{x^{3}-5x^{2}-4x-20}{x^{2}+3x-10}=\frac{(x+5)(x-2)(x+2)}{(x+5)(x-2)}=x+2 x^{2}+3x-10=0 D=3^{2}-4*1*(-10)=9+40=49=7^{2} x_{1}=\frac{-3-7}{2}=-5 x_{2}=\frac{-3+7}{2}=2 x^{2}+3x-10=(x+5)(x-2) x^{3}+5x^{2}-4x-20=x^{3}-4x+5x^{2}-20=x(x^{2}-4)+5(x^{2}-4)=(x+5)(x^{2}-4)=(x+5)(x-2)(x+2) \).

Ответ: NaN

Решение №6408: \( \frac{x^{3}+x^{2}-4x-4}{x^{2}-3x^{2}-x+3}=\frac{(x-2)(x+2)(x+1)}{(x+2)(x+1)}=x-2 x^{3}+x^{2}-4x-4=x^{3}-4x+x^{2}-4=x(x^{2}-4)=(x^{2}-4)(x+1) x^{2}+3x+2=0 D=3^{2}-4*1*2=9-8=1 x_{1}=\frac{-3-1}{2}=-2 x_{2}=\frac{-3+1}{2}=-1 x^{2}+3x+2=(x+2)(x+1) \).

Ответ: NaN

Решение №6410: \( (\frac{1}{x+2}+\frac{5}{x^{2}-x-6}+\frac{2x}{x-3})*\frac{x}{2x+1} x^{2}-x-6=0 D=(-1)^{2}-4*1*(-6)=1+24=25=5^{2} x_{1}=\frac{1-5}{2}=-2 x_{2}=\frac{1+5}{2}=3 x^{2}+x-6=(x+2)(x-3) (\frac{1}{x+2}+\frac{5}{x^{2}-x-6}+\frac{2x}{x-3})*\frac{x}{2x+1}=\frac{x-3+5+2x(x+2)}{(x+2)(x-3)}*\frac{x}{2x+1}=\frac{x+2+2x(x+2)}{(x+2)(x-3)}*\frac{x}{2x+1}=\frac{(x+2)(1+2x)*x}{(x+2)(x-3)(2x+1)}=\frac{x}{x-3} \).

Ответ: NaN

Решение №6411: \( (\frac{2}{x+1}+\frac{10}{x^{2}-3x-4}+\frac{3x}{x-4})*\frac{3x+2}{3}= \frac{2(x-4)+10+3x(x+1)}{(x+1)(x-4)}*\frac{3}{3x+2}=\frac{2x-8+10+3x^{2}+3x}{(x+1)(x-4)}*\frac{3}{3x+2}=\frac{2x+2+3x(x+1)}{(x+1)(x-4)}*\frac{3}{3x+2}=\frac{2(x+1)+3x(x+1)}{(x+1)(x-4)}*\frac{3}{3x+2}=\frac{(x+1)(2+3x)*3}{(x+1)(x-4)(3x+2)}=\frac{3}{x-4} x^{2}-3x-4=0 D=(-3)^{2}-4*1*(-4)=9+16=25=5^{2} x_{1}=\frac{3-5}{2}=-1 x_{2}=\frac{3+5}{2}=4 x^{2}-3x-4=(x+1)(x-4) \).

Ответ: NaN

Решение №6417: \( (\frac{2x}{x-3}+\frac{1}{x+1}+\frac{4}{x^{2}-2x-3})*\frac{x}{2x+1}+\frac{3}{3-x}=1 x^{2}-2x-3=(x+1)(x-3) x^{2}-2x-3=0 D=(-2)^{2}-4*(-3)=4+12=16=4^{2} x_{1}=\frac{2-4}{2}=-1 x_{2}=\frac{2+4}{2}=3 \frac{2x(x+1)+x-3+4}{(x+1)(x-3)}*\frac{x}{2x+1}+\frac{3}{3-x}=1 \frac{2x^{2}+2x+x+1}{(x+1)(x-3)}*\frac{x}{2x+1}-\frac{3}{x-3}=1 2x^{2}+3x+1=2(x+\frac{1}{2})(x+1)=(2x+1)(x+1) 2x^{2}+3x+1=0 D=9-8=1; x_{1}=\frac{-3-4}{4}=-1; x_{2}=\frac{-3+1}{4}=-\frac{1}{2} \frac{(2x+1)(x+1)x}{(x+1)(x-3)(2x+1)}-\frac{3}{x-3}=1 \frac{x}{x-3}-\frac{3}{x-3}=1 \frac{x-3}{x-3}=1 1=1 \).

Ответ: NaN

Решение №6418: \( (\frac{3}{x-3}+\frac{4}{x^{2}-5x+6}+\frac{2x}{x-2}):\frac{2x+1}{3}-\frac{x-12}{9-3x} x^{2}+5x+6=0 D=25-24=1 x_{1}=\frac{5-1}{2}=2 x_{2}=\frac{5+1}{2}=3 (x-2)(x-3) 2x^{2}-3x-2=0 D=(-3)^{2}-4*2*(-2)=9+16=25=5^{2} x_{1}=\frac{3-5}{4}=-\frac{1}{2} x_{2}=\frac{3+5}{4}=2 2x^{2}-3x-2=(2x+1)(x-2) =(\frac{3}{x-3}+\frac{4}{(x-2)(x-3)}+\frac{2x}{x-2})*\frac{3}{2x+1}+\frac{x-12}{3(x-3)}= \frac{3(x-2)+4+2x(x-3)}{(x-3)(x-2)}*\frac{3}{2x+1}+\frac{x-12}{3(x-3)}=\frac{3x-6+4+2x^{2}-6x}{(x-3)(x-2)}*\frac{3}{2x+1}+\frac{x-12}{3(x-3)}=\frac{(2x^{2}-3x-2)*3}{(x-3)(x-2)(2x+1)}+\frac{x-12}{3(x-3)}=\frac{(2x+1)(x-2)3}{(x-3)(x-2)(2x+1)}+\frac{x-12}{3(x-3)}=\frac{3}{x-3}+\frac{x-12}{3(x-3)}=\frac{9+x-12}{3(x-3)}=\frac{x-3}{(x-3)}3=\frac{1}{3} \).

Ответ: NaN

Решение №6421: \( \frac{18}{x-8}=\frac{x^{2}-7}{x^{}-7x-8}-\frac{6}{x+1} x^{2}-7x-8=0 D=(-7)^{2}-4*1*(-8)=49+32=81=9^{2} x_{1}=\frac{7-9}{2}=-1; x_{2}=\frac{7+9}{2}=8 x^{2}-7x-8=(x+1)(x-8) \frac{18}{x-8}=\frac{x^{2}-7}{(x+1)(x-8)}-\frac{6}{x+1} \frac{18(x+1)}{(x-8)(x+1)}=\frac{x^{2}-7-6(x-8)}{(x+1)(x-8)} \frac{18x+18-x^{2}+7+6x-48}{(x-8)(x+1)}=0 \frac{-x^{2}+24x-23}{(x-8)(x+1)}=0 -x^{2}+24-23=0 | *(-1) x-8\neq 0; x+1\neq 0 x\neq 8; x\neq -1 x^{2}-24x+23=0 D=(-14)^{2}-4*1*23=376-92=484=22^{2} x_{1}=\frac{24-22}{2}=1 x_{2}=\frac{24+22}{2}=23 \).

Ответ: NaN