Bài 1

b) \(3^x.5=405\)

\(3^x=405:5\)

\(3^x=81\)

\(3^x=3^4\)

\(x=4\)

c) \(9.2^x-5.2^x=32\)

\(2^x.\left(9-5\right)=32\)

\(2^x.4=32\)

\(2^x=32:4\)

\(2^x=8\)

\(2^x=2^3\)

\(x=3\)

h) \(5^{x+2}+5^{x+1}=750\)

\(5^{x+1}.\left(5+1\right)=750\)

\(5^{x+1}.6=750\)

\(5^{x+1}=750:6\)

\(5^{x+1}=125\)

\(5^{x+1}=5^3\)

\(x+1=3\)

\(x=3-1\)

\(x=2\)

`2,`

c)

`(x - \frac{1}{2})^3 = -8`

`\Rightarrow (x - \frac{1}{2})^3 = (-2)^3`

`\Rightarrow x - \frac{1}{2} = -2`

`\Rightarrow x = -2 + \frac{1}{2}`

`\Rightarrow x = -\frac{3}{2}`

Vậy, `x = \frac{-3}{2}`

d)

`(5x - 3)^4 = 256`

`\Rightarrow (5x - 3)^4 = (+-4)^4`

`\Rightarrow`\(\left[{}\begin{matrix}5x-3=4\\5x-3=-4\end{matrix}\right.\)

`\Rightarrow`\(\left[{}\begin{matrix}5x=7\\5x=-1\end{matrix}\right.\)

`\Rightarrow`\(\left[{}\begin{matrix}x=\dfrac{7}{5}\\x=-\dfrac{1}{5}\end{matrix}\right.\)

Vậy, `x \in`\(\left\{-\dfrac{1}{5};\dfrac{7}{5}\right\}\)

f)

\(\dfrac{\left(x-2\right)^2}{7}=\dfrac{49}{x-2}\)

`\Rightarrow (x-2)^2 * (x - 2) = 7*49`

`\Rightarrow (x - 2)^3 = 7*7^2`

`\Rightarrow (x - 2)^3 = 7^3`

`\Rightarrow x - 2 = 7`

`\Rightarrow x = 7 + 2`

`\Rightarrow x = 9`

Vậy, `x = 9`

g)

`(x - \frac{1}{2})^3 = \frac{1}{27}`

`\Rightarrow (x - \frac{1}{2})^3 = (\frac{1}{3})^3`

`\Rightarrow x - \frac{1}{2} = \frac{1}{3}`

`\Rightarrow x = \frac{1}{3} + \frac{1}{2}`

`\Rightarrow x = \frac{5}{6}`

Vậy, `x = \frac{5}{6}.`

\(=4.\left(-\dfrac{1}{8}\right)-2.\dfrac{1}{4}-\dfrac{3}{2}+1=\)

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

= 4 . -1/8 - 2 . -1/4 + 3 . -1/2 + 1

= -1/2 - -1/2 + -3/2 + 1

= -1/2

\(\dfrac{1}{5}:\left(x-3\right)+\dfrac{1}{2}=1\dfrac{1}{8}\\ \Rightarrow\dfrac{1}{5}:\left(x-3\right)=\dfrac{9}{8}-\dfrac{1}{2}\\ \Rightarrow\dfrac{1}{5}:\left(x-3\right)=\dfrac{9}{8}-\dfrac{4}{8}\\ \Rightarrow\dfrac{1}{5}:\left(x-3\right)=\dfrac{5}{8}\\ \Rightarrow x-3=\dfrac{1}{5}:\dfrac{5}{8}\\ \Rightarrow x-3=\dfrac{8}{25}\\ \Rightarrow x=\dfrac{8}{25}+3\\ \Rightarrow x=\dfrac{83}{25}\)

\(\dfrac{1}{5}:\left(x-3\right)+\dfrac{1}{2}=1\dfrac{1}{8}\)

\(\dfrac{1}{5}:\left(x-3\right)+\dfrac{1}{2}=\dfrac{9}{8}\)

\(\dfrac{1}{5}:\left(x-3\right)=\dfrac{9}{8}-\dfrac{1}{2}=\dfrac{9}{8}-\dfrac{4}{8}\)

\(\dfrac{1}{5}:\left(x-3\right)=\dfrac{5}{8}\)

\(x-3=\dfrac{1}{5}:\dfrac{5}{8}=\dfrac{1}{5}.\dfrac{8}{5}\)

\(x-3=\dfrac{8}{25}\)

\(x=\dfrac{8}{25}+3=\dfrac{8}{25}+\dfrac{75}{25}\)

\(x=\dfrac{83}{25}\)

Nghiệm của đa thức trên là: x = 9

Ngiệm là 9 nha

Bạn xem lại đề bài

\(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{2a}{2b}=\dfrac{3c}{3d}=\dfrac{2a+3c}{2b+3d}=\dfrac{2a-3c}{2b-3d}\)

\(\Rightarrow\dfrac{2a+3c}{2a-3c}=\dfrac{2b+3d}{2b-3d}\)

\(\Rightarrow dpcm\)

\(\dfrac{y}{5}=\dfrac{z}{6}\Rightarrow z=\dfrac{5y}{6}\)

mà \(z-y=40\)

\(\Rightarrow\dfrac{5y}{6}-y=40\)

\(\Rightarrow-\dfrac{y}{6}=40\)

\(\Rightarrow y=-240\Rightarrow z=40+y=40-240=-200\)

\(\dfrac{x}{3}=\dfrac{y}{4}\Rightarrow x=\dfrac{3y}{4}=\dfrac{3.\left(-240\right)}{4}=-180\)

Vậy \(\left\{{}\begin{matrix}x=-180\\y=-240\\z=-200\end{matrix}\right.\)

\(S=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{78.79.80}\)

\(\Rightarrow S=\dfrac{79\left(79+3\right)}{4\left(79+1\right)\left(79+2\right)}\)

\(S=\dfrac{79.82}{4.80.81}=\dfrac{79.41}{160.81}=\dfrac{3239}{12960}\)

\(\text{2.24.25+3.31.16+6.2.8.17}\)

\(=\text{2.6.4.25+3.31.16+6.16.17}\)

\(=\text{12.100+16.3(31+2.17)}\)

\(=\text{1200+48(31+34)}=1200+48.65=1200+3120=4320\)

\(A=\dfrac{1}{3}-\left[\left(-\dfrac{5}{4}\right)-\left(\dfrac{1}{4}+\dfrac{3}{8}\right)\right]\)

\(A=\dfrac{1}{3}-\left[\dfrac{-5}{4}-\dfrac{5}{8}\right]=\dfrac{1}{3}-\left(\dfrac{-15}{8}\right)\)

\(A=\dfrac{53}{24}\)

=> A > 2

=> C là đáp án đúng

A