7^5:7^3-2^2x2

=7^2-2^3

=49-8

=41

7⁵ : 7³ - 2² . 2

= 7^5-3 - 2² . 2

= 7² - 2² . 2

= 49 - 4 . 2

= 49 - 8

= 41

7⁵ : 7³ - 2² . 2

= 7^{( 5 - 3 )} - 2^{( 2 + 1 )} 

= 7² - 2³

= 49 - 8

= 41

Câu 1 :

a. \(4x-5=23\\ \Leftrightarrow4x=23+5\\ \Leftrightarrow4x=28\\ \Leftrightarrow x=7\)

b. 

|-2x|=5x+14

 Nếu - 2x > 0 => x < 0 thì |-2x|= - 2x, ta có pt: -2x = 5x+14

 <=> - 2x = 5x + 14

 <=> - 2x - 5x = 14

 <=> - 7x = 14

 <=> x = - 2 (thoã mãn)

 Nếu - 2x < 0 => x > 0 thì |-2x|= = -(- 2x) = 2x.

Ta có pt: 2x = 5x + 14

 <=> - 3x = 14

<=> x = \(-\dfrac{14}{3}\)
 Vậy pt có nghiệm x = - 2

c) \(\dfrac{x+1}{x-1}-\dfrac{1}{x+1}=\dfrac{x^2+2}{x^2-1}\\ ĐKXĐ:x\ne1;x\ne-1\\ \Leftrightarrow\dfrac{\left(x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\dfrac{1\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{x^2+2}{\left(x-1\right)\left(x+1\right)}\\ \Leftrightarrow x^2+x+x+1-x+1=x^2+2\\ \Leftrightarrow x^2+x+x-x-x^2=2-1-1\\ \Leftrightarrow x=0\left(nhận\right)\)

\(a,4x-5=23\)

\(\Leftrightarrow4x=23+5\)

\(\Leftrightarrow4x=28\)

\(\Leftrightarrow x=7\)

\(b,\left|-2x\right|=5x+14\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=5x+14\\2x=-5x-14\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-3x-14=0\\7x+14=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-3x=14\\7x=-14\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{14}{3}\\x=-2\end{matrix}\right.\)

Vậy \(S=\left\{-\dfrac{14}{3};-2\right\}\)

\(c,\Leftrightarrow\dfrac{\left(x+1\right)\left(x+1\right)-x+1-x^2-2}{x^2-1}=0\)

\(\Leftrightarrow x^2+x+x+1-x+1-x^2-2=0\)

\(\Leftrightarrow x=0\)

Vậy \(S=\left\{0\right\}\)

a) \(4x-5=23\)

    \(4x=23+5\)

      \(4x=28\)

        \(x=7\)

b) \(\left|-2x\right|=5x+14\)

 \(\Leftrightarrow\)   \(-2x-5=14\)

\(\Leftrightarrow\)    \(-7x=14\)

\(\Leftrightarrow\)         \(x=-2\)

\(\Leftrightarrow\)    \(-2x=-\left(5x+14\right)\)

\(\Leftrightarrow\)    \(-2x=-\left(5x-14\right)\)

\(\Leftrightarrow\)  \(-2x+5x=-14\)

 \(\Leftrightarrow\)    \(3x=-14\)

 \(\Leftrightarrow\) \(x=-\dfrac{14}{3}\) \(\left(\text{vô lí}\right)\)

  \(\Leftrightarrow x=-2\)   

c) \(\dfrac{x+1}{x-1}-\dfrac{1}{x+1}=\dfrac{x^2+2}{x^2-1}\)

 \(\Leftrightarrow\) \(\dfrac{x+1}{x-1}+\dfrac{-1}{x+1}=\dfrac{x^2+2}{\left(x+1\right)\left(x-1\right)}\)

 \(\Leftrightarrow\left(x+1\right)\left(x+1\right)+\left(-1\right)\left(x-1\right)=x^2+2\)

\(\Leftrightarrow x^2+x+2=x^2+2\)

\(\Leftrightarrow x+2=2\)

\(\Leftrightarrow x=0\)

a,

A=1−3−5−7−9−...−97−99a)A=1−3−5−7−9−...−97−99 

=1−(3+5+7+...+99)=1−(3+5+7+...+99)

=1−(99+3).[(99−3):2+1]2=1−(99+3).[(99−3):2+1]2
=1−2499=−2498=1−2499=−2498

b)B=1+3−5−7+9+...+97−99b)B=1+3−5−7+9+...+97−99
=(−8)+(−8)+(−8)+...+(−8)+97−99=(−8)+(−8)+(−8)+...+(−8)+97−99
=(−8).12+(−2)=−98=(−8).12+(−2)=−98

c)C=1−3−5+7+9−11−13+15+...+97−99c)C=1−3−5+7+9−11−13+15+...+97−99
=0+0+0+0+0+...+0−99=0+0+0+0+0+...+0−99
=−99

Gọi vận tốc thực là x

Độ dài quãng đường AB là 4(x+2)

Theo đề, ta có phươg trình:

4(x+2)=5(x-2)

=>5x-10=4x+8

=>x=18

Vậy: Độ dài quãng đường là 80km

Gọi vận tốc thực là x(km/h)

Độ dài quãng đường là 4(x+2)

Theo đề, ta có phương trình:

4(x+2)=5(x-2)

=>5x-10=4x+8

=>x=18

Vậy: Độ dài quãng đường là 80km

a)\(\frac{7}{1}.\frac{5}{9}.\frac{11}{35}=\frac{7.5.11}{9.5.7}=\frac{11}{9}\)

b) \(\frac{3}{5}.\frac{4}{23}.\frac{5}{6}=\frac{3.2.2.5}{5.23.3.2}=\frac{2}{23}\)

c) \(\frac{5}{2}.\frac{7}{4}.\frac{2}{7}=\frac{5.7.2}{2.7.4}=\frac{5}{4}\)

d)  \(\frac{19}{23}.\frac{12}{17}.\frac{85}{24}=\frac{19.12.5.17}{23.17.12.2}=\frac{19.5}{23.2}=\frac{95}{46}\)

Tính

A. \(\frac{7}{1}x\frac{5}{9}x\frac{11}{35}=\frac{7x5x11}{1x9x35}=\frac{11}{9}\)

B. \(\frac{3}{5}x\frac{4}{23}x\frac{5}{6}=\frac{3x4x5}{5x23x6}=\frac{2}{23}\)

C. \(\frac{5}{2}x\frac{7}{4}x\frac{2}{7}=\frac{5x7x2}{2x4x7}=\frac{35}{28}\)

D. \(\frac{19}{23}x\frac{12}{17}x\frac{85}{24}=\frac{19x12x85}{23x17x24}=\frac{4845}{2346}\)

\(A=3\sqrt{2}+5\sqrt{8}-2\sqrt{50}\)

\(=3\sqrt{2}+10\sqrt{2}-10\sqrt{2}\)

\(=3\sqrt{2}\)

\(B=\dfrac{1}{3+\sqrt{5}}+\dfrac{1}{3-\sqrt{5}}\)

\(=\dfrac{3-\sqrt{5}}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}+\dfrac{3+\sqrt{5}}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}\)

\(=\dfrac{3-\sqrt{5}+3+\sqrt{5}}{9-5}\)

\(=\dfrac{3}{2}\)

\(A=3\sqrt{2}+5\sqrt{8}-2\sqrt{50}\)

\(A=3\sqrt{2}+10\sqrt{2}-10\sqrt{2}=3\sqrt{2}\)

\(B=\dfrac{1}{3+\sqrt{5}}+\dfrac{1}{3-\sqrt{5}}\)

\(B=\dfrac{3-\sqrt{5}+3+\sqrt{5}}{9-5}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(C=\sqrt{7-4\sqrt{3}}+\sqrt{12+6\sqrt{3}}\)

\(C=\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(3+\sqrt{3}\right)^2}\)

\(C=2-\sqrt{3}+3+\sqrt{3}=5\)