Bài 2:

a,4x25x0,25x\(\frac{1}{5}\) x \(\frac{1}{2}\) x 2

 =4x25x0,25x0,2x0,5x2

 =(4x0,25)+(25x0,2)+(0,5x2)

 =      1     +     5             1

 =7

X + 1/2 + X + 1/4 + X + 1/8 + X + 1/8 +X +1/16 

= X + 8/16 + X + 4/16 + X + 2/16 + X + 2/16 +X + 1/16 

= X + ( 8/16 + 4/16 + 2/16 + 2/16 )  + X +1/16 

= X + 1 + X + 1/16 

= X + ( 1 + 1/16 ) 

=  X + 1 VÀ 1/16 

1) x-12=(-8)+(-17)
    x-12=(-25)
    x      = (-25)+12
    x      = (-13)

Trả lời

\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=\frac{23}{16}\)

\(\Leftrightarrow\left(x+x+x+x\right)+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)=\frac{23}{16}\)

\(\Leftrightarrow4x+\left(\frac{8}{16}+\frac{4}{16}+\frac{2}{16}+\frac{1}{16}\right)=\frac{23}{16}\)

\(\Leftrightarrow4x+\frac{8+4+2+1}{16}=\frac{23}{16}\)

\(\Leftrightarrow4x+\frac{15}{16}=\frac{23}{16}\)

\(\Leftrightarrow4x=\frac{23}{16}-\frac{15}{16}\)

\(\Leftrightarrow4x=\frac{8}{16}\)

\(\Leftrightarrow4x=\frac{1}{2}\)

\(\Leftrightarrow x=\frac{1}{2}:4\)

\(\Leftrightarrow x=\frac{1}{8}\)

Vậy x=\(\frac{1}{8}\)

\(\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=\frac{23}{16}\)

\(\Leftrightarrow\left(x+x+x+x\right)+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)=\frac{23}{16}\)

\(\Leftrightarrow4x+\left(\frac{8+4+2+1}{16}\right)=\frac{23}{16}\)

\(\Leftrightarrow4x+\frac{15}{16}=\frac{23}{16}\)

\(\Leftrightarrow4x=\frac{23}{16}-\frac{15}{16}\)

\(\Leftrightarrow4x=\frac{1}{2}\)

\(\Leftrightarrow x=\frac{1}{2}:4\)

\(\Leftrightarrow x=\frac{1}{8}\)

2:

\(A=\dfrac{x_2-1+x_1-1}{x_1x_2-\left(x_1+x_2\right)+1}\)

\(=\dfrac{3-2}{-7-3+1}=\dfrac{1}{-9}=\dfrac{-1}{9}\)

B=(x1+x2)^2-2x1x2

=3^2-2*(-7)

=9+14=23

C=căn (x1+x2)^2-4x1x2

=căn 3^2-4*(-7)=căn 9+28=căn 27

D=(x1^2+x2^2)^2-2(x1x2)^2

=23^2-2*(-7)^2

=23^2-2*49=431

D=9x1x2+3(x1^2+x2^2)+x1x2

=10x1x2+3*23

=69+10*(-7)=-1

\(\dfrac{11}{8}:x-\dfrac{2}{5}+-\dfrac{1}{6}=-\dfrac{1}{5}\\ =>\dfrac{11}{8}:x-\dfrac{2}{5}=-\dfrac{1}{5}-\left(-\dfrac{1}{6}\right)\\ =>\dfrac{11}{8}:x-\dfrac{2}{5}=-\dfrac{1}{5}+\dfrac{1}{6}\\ =>\dfrac{11}{8}:x-\dfrac{2}{5}=-\dfrac{6}{30}+\dfrac{5}{30}\\ =>\dfrac{11}{8}:x-\dfrac{2}{5}=-\dfrac{1}{30}\\ =>\dfrac{11}{8}:x=-\dfrac{1}{30}+\dfrac{2}{5}\\ =>\dfrac{11}{8}:x=-\dfrac{1}{30}+\dfrac{12}{30}\\ =>\dfrac{11}{8}:x=\dfrac{11}{30}\\ =>x=\dfrac{11}{8}:\dfrac{11}{30}\\ =>x=\dfrac{11}{8}.\dfrac{30}{11}\\ =>x=\dfrac{30}{8}\\ =>x=\dfrac{15}{4}\\ \dfrac{4}{7}x-\dfrac{1}{3}x+\left(-\dfrac{16}{21}\right)=-\dfrac{2}{3}\\ =>\left(\dfrac{4}{7}-\dfrac{1}{3}\right)x=-\dfrac{2}{3}-\left(-\dfrac{16}{21}\right)\\ =>\left(\dfrac{12}{21}-\dfrac{7}{21}\right)x=-\dfrac{2}{3}+\dfrac{16}{21}\\ =>\dfrac{5}{21}x=-\dfrac{14}{21}+\dfrac{16}{21}\\ =>\dfrac{5}{21}x=\dfrac{2}{21}\\ =>x=\dfrac{2}{21}:\dfrac{5}{21}\)

\(=>x=\dfrac{2}{21}.\dfrac{21}{5}\\ =>x=\dfrac{2}{5}\\ -\dfrac{11}{12}x+\dfrac{15}{2}\left(x+-\dfrac{1}{5}\right)=\dfrac{67}{8}\\ =>-\dfrac{11}{12}x+\dfrac{15}{2}.x-\dfrac{1}{5}=\dfrac{67}{8}\\ =>\left(-\dfrac{11}{12}+\dfrac{15}{2}\right)x=\dfrac{67}{8}+\dfrac{1}{5}\\ =>\left(-\dfrac{11}{12}+\dfrac{90}{12}\right)x=\dfrac{335}{40}+\dfrac{8}{40}\\ =>\dfrac{79}{12}x=\dfrac{343}{40}\\ =>x=\dfrac{343}{40}:\dfrac{79}{12}\\ =>x=\dfrac{343}{40}.\dfrac{12}{79}\\ =>x=\dfrac{343.12}{40.79}\\ =>x=\dfrac{343.3}{10.79}\\ =>x=\dfrac{1029}{790}\)

4x=1-(1/16+1/4+1/5+1/2)=0,0625=1/16

x=1/16/4=1/64

hỏi google ấy 

Lời giải:

Để PT có 2 nghiệm $x_1,x_2$ thì:

$\Delta'=(m+1)^2-(m^2-1)>0\Leftrightarrow 2m+2>0\Leftrightarrow m>-1$

Áp dụng định lý Viet:

$x_1+x_2=2(m+1)$ và $x_1x_2=m^2-1$

Khi đó, để $x_1^2+x_2^2=x_1x_2+8$

$\Leftrightarrow (x_1+x_2)^2-2x_1x_2=x_1x_2+8$

$\Leftrightarrow (x_1+x_2)^2=3x_1x_2+8$

$\Leftrightarrow 4(m+1)^2=3(m^2-1)+8$

$\Leftrightarrow m^2+8m-1=0$

$\Leftrightarrow m=-4\pm \sqrt{17}$. Vì $m>-1$ nên $m=-4+\sqrt{17}$

(x+1/2)+(x+1/4)+(x+1/8)+(x+1/16)=1

(x+x+x+x)+(1/2+1/4+1/8+1/16)=1

4x+(1/2+1/4+1/8+1/16)=1

4x+15/16=1

4x=1-15/16

4x=1/16

x=1/16:4

x=1/64

X=1/46