8x - 1 )^2x + 1 = 5^2x + 1

    8x - 1^2x + 1 = 5^2x + 1

⇒ 8x - 1              = 5 

    8x - 1 + 1        = 5 + 1 ( Cộng 1 vào cả 2 vế của phương trình )

    8x                    = 5 + 1

    8x                    = 6

⇒ 8x/8 = 6/8 ( Chia cả hai vế của phương trình cho cùng một số hạng )

⇒ x                      = 6/8

⇒ x                      = 3/4 ( rút gọn )

Vậy x = 3/4

76 phần 255

\(\dfrac{2x-3}{5}=\dfrac{x-2}{4}\)
\(\Rightarrow\left(2x-3\right)\cdot4=\left(x-2\right)\cdot5\)
\(\Rightarrow8x-12=5x-10\)
\(\Rightarrow8x-5x=-10+12\)
\(\Rightarrow3x=2\)
\(\Rightarrow x=\dfrac{2}{3}\)
Vậy \(x=\dfrac{2}{3}\)
#kễnh

\(\dfrac{2x-3}{5}=\dfrac{x-2}{4}\)

\(\Leftrightarrow4\left(2x-3\right)=5\left(x-2\right)\)

\(\Leftrightarrow8x-12=5x-10\)

\(\Leftrightarrow3x=2\)

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

\(\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{5}{7}-\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{11}{13}+\dfrac{13}{15}+\dfrac{11}{13}-\dfrac{9}{11}+\dfrac{7}{9}-\dfrac{5}{7}+\dfrac{3}{5}-\dfrac{1}{3}\)
\(=\left(\dfrac{1}{3}-\dfrac{1}{3}\right)-\left(\dfrac{3}{5}-\dfrac{3}{5}\right)+\left(\dfrac{5}{7}-\dfrac{5}{7}\right)-\left(\dfrac{7}{9}-\dfrac{7}{9}\right)+\left(\dfrac{9}{11}-\dfrac{9}{11}\right)-\left(\dfrac{11}{13}-\dfrac{11}{13}\right)+\dfrac{13}{15}\)
\(=\dfrac{13}{15}\)

$\genfrac{}{}{0ex}{}{1}{3}-\genfrac{}{}{0ex}{}{3}{5}+\genfrac{}{}{0ex}{}{5}{7}-\genfrac{}{}{0ex}{}{7}{9}+\genfrac{}{}{0ex}{}{9}{11}-\genfrac{}{}{0ex}{}{11}{13}+\genfrac{}{}{0ex}{}{13}{15}+\genfrac{}{}{0ex}{}{11}{13}-\genfrac{}{}{0ex}{}{9}{11}+\genfrac{}{}{0ex}{}{7}{9}-\genfrac{}{}{0ex}{}{5}{7}+\genfrac{}{}{0ex}{}{3}{5}-\genfrac{}{}{0ex}{}{1}{3}$
$=\left(\genfrac{}{}{0ex}{}{1}{3}-\genfrac{}{}{0ex}{}{1}{3}\right)-\left(\genfrac{}{}{0ex}{}{3}{5}-\genfrac{}{}{0ex}{}{3}{5}\right)+\left(\genfrac{}{}{0ex}{}{5}{7}-\genfrac{}{}{0ex}{}{5}{7}\right)-\left(\genfrac{}{}{0ex}{}{7}{9}-\genfrac{}{}{0ex}{}{7}{9}\right)+\left(\genfrac{}{}{0ex}{}{9}{11}-\genfrac{}{}{0ex}{}{9}{11}\right)-\left(\genfrac{}{}{0ex}{}{11}{13}-\genfrac{}{}{0ex}{}{11}{13}\right)+\genfrac{}{}{0ex}{}{13}{15}$
$=\genfrac{}{}{0ex}{}{13}{15}$

 

`# \text {Ryo}`

So sánh ạ?

\(2^{225}\text{ và }3^{150}\)

Ta có:

\(2^{225}=2^{3\cdot75}=\left(2^3\right)^{75}=8^{75}\\ 3^{150}=3^{2\cdot75}=\left(3^2\right)^{75}=9^{75}\)

Vì `9 > 8 \Rightarrow`\(9^{75}>8^{75}\)

\(\Rightarrow2^{225}< 3^{150}\)

2²²⁵ = (2³)⁷⁵ = 8⁷⁵

3¹⁵⁰ = (3²)⁷⁵ = 9⁷⁵

Do 8 < 9 nên 8⁷⁵ < 9⁷⁵

Vậy 2²²⁵ < 3¹⁵⁰

a) 17/20 = 323/380

18/19 = 360/380

Do 323 < 360 nên 323/380 < 360/380

Vậy 17/20 < 18/19

b) 19/18 = 1 + 1/18

2023/2022 = 1 + 1/2022

Do 18 < 2022 nên 1/18 > 1/2022

1 + 1/18 > 1 + 1/2022

Vậy 19/18 > 2023/2022

c) 13/17 = 455/595

135/175 = 27/35 = 459/595

Do 455 < 459 nên 455/595 < 459/595

Vậy 13/17 < 135/175

d) 53/63 = 11236/13356

535/636 = 11235/13356

Do 11236 > 11235 nên 11236/13356 > 11235/13356

Vậy 53/63 > 535/636

e) 13/15 = 65/75

22/25 = 66/75

Do 65 < 66 nên 65/75 < 66/75

Vậy 13/15 < 22/25