Ответы и объяснения

2013-03-28T15:45:47+04:00

1)\frac{4-x}{x-5}>\frac{1}{1-x}

(4-x)(1-x)>x-5

4-4x-x+x^2-x+5>0

x^2-6x+9>0

x^2-6x+9=0

D=6^2-4*1*9=36-36=0

x=\frac{6+0}{2}=3

x>3

 

3)\frac{(13,75+9\frac{1}{6})*1,2}{(10,3-8\frac{1}{2})*\frac{5}{9}}+\frac{(6,8-3\frac{3}{5})*5\frac{5}{6}}{(3\frac{2}{3}-3\frac{1}{6})*56}-27\frac{1}{6}=149,5

 

{(13,75+9\frac{1}{6})*1,2}=176

1) 13,75+9\frac{1}{6}=\frac{275}{2}+\frac{55}{6}=\frac{880}{6}=\frac{440}{3}

2)\frac{440}{3}*1,2=\frac{440}{3}*\frac{6}{5}=176

 

(10,3-8\frac{1}{2})*\frac{5}{9}=1

1) 10,3-8\frac{1}{2}=10,3-8,5=1,8

2)1,8*\frac{5}{9}=\frac{9}{5}*\frac{5}{9}=1

 

(6,8-3\frac{3}{5})*5\frac{5}{6}=\frac{56}{3}

1)6,8-3\frac{3}{5}=6,8-3,6=3,2

2)3,2*5\frac{5}{6}=\frac{16}{5}*\frac{35}{6}=\frac{56}{3}

 

(3\frac{2}{3}-3\frac{1}{6})*56=28

1) 3\frac{2}{3}-3\frac{1}{6}=\frac{11}{3}-\frac{19}{6}=\frac{3}{6}=0,5

2) 0,5*56=28

 

\frac{56}{3}:\frac{28}{1}=\frac{56}{3}*\frac{1}{28}=\frac{2}{3}

 

1) 176+\frac{2}{3}=176\frac{2}{3}

 

2)176\frac{2}{3}-27\frac{1}{6}=149\frac{1}{2}=149,5

 

4) a)/2-x/=5-4x

        2-x=5-4x

       -x+4x=5-2        

       3x=3

       x=1,-1

 

б)\frac{6}{x^2-4x+3}-\frac{13-7x}{1-x}=\frac{3}{x-3}

\frac{6}{x^2-4x+3}+\frac{13-7x}{x-1}=\frac{3}{x-3} берем общий знаменатель(x-1)(x-3)

6+(x-3)(13-7x)=3(x-1)

6+13x-7x^2-39+21x-3x+3=0

-7x^2+31x-30=0

7x^2-31x+30=0

D=31^2-4*7*30=961-840=121

\sqrt{D}=11

x1=\frac{31-11}{2*7}=\frac{10}{7}

x2=\frac{31+11}{14}=\frac{42}{14}=3

 

6)(\frac{\sqrt{x}+\sqrt{y}}{\sqrt{x}-\sqrt{y}}-\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}})*(\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{y}})=\frac{4}{(\sqrt{x}+\sqrt{y})}

 

1)\frac{\sqrt{x}+\sqrt{y}}{\sqrt{x}-\sqrt{y}}-\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}=\frac{(\sqrt{x}+\sqrt{y})(\sqrt{x}+\sqrt{y})-(\sqrt{x}-\sqrt{y})(\sqrt{x}-\sqrt{y})}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}=\frac{x+\sqrt{xy}+y-x+\sqrt{xy}+\sqrt{xy}-y}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y}}=\frac{4\sqrt{xy}}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}

 

2)\frac{1}{\sqrt{y}}-\frac{1}{\sqrt{x}}=\frac{\sqrt{x}-\sqrt{y}}{\sqrt{yx}}

 

3)\frac{4\sqrt{xy}}{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}*\frac{\sqrt{x}-\sqrt{y}}{\sqrt{yx}}=\frac{4}{\sqrt{x}+\sqrt{y}}