Question

[Đỗ Anh Chí]

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Answer 1

[Member lỗi thời :>>]

a) ( x - 1 )³ = 27 

=> ( x - 1 )³ = 3³

=> x - 1 = 3

=> x = 4

b) x² + x = 0

=> x . ( x + 1 ) = 0

\(\Rightarrow\orbr{\begin{cases}x=0\\x+1=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x=-1\end{cases}}\)

c) ( 2x + 1 )² = 25 

=> ( 2x + 1 )² = 5² = ( -5 )²

\(\Rightarrow\orbr{\begin{cases}2x+1=5\\2x+1=-5\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}2x=4\\2x=-6\end{cases}}\Rightarrow\orbr{\begin{cases}x=2\\x=-3\end{cases}}\)

d) ( 2x - 3 )² = 36

=> ( 2x - 3 )² = 6² = ( -6 )²

\(\Rightarrow\orbr{\begin{cases}2x-3=6\\2x-3=-6\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}2x=9\\2x=-3\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{9}{2}\\x=\frac{-3}{2}\end{cases}}\)

e) 5^x+2 = 625

=> 5^x+2 = 5⁴

=> x + 2 = 4

=> x = 2

f) ( x - 1 )^x+2 = ( x - 1 )^x+4

=> ( x - 1 )^x+4 - ( x - 1 )^x+2 = 0

=> ( x - 1 )^x+2 . [ ( x - 1 )² - 1 ] = 0

\(\Rightarrow\orbr{\begin{cases}\left(x-1\right)^{x+2}=0\\\left(x-1\right)^2-1=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x-1=0\\\left(x-1\right)^2=1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=1\\x-1\in\left\{-1;1\right\}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=1\\x\in\left\{0;2\right\}\end{cases}}\)

g) ( 2x - 1 )³ = 8

=> ( 2x - 1 )³ = 2³

=> 2x - 1 = 2

=> 2x = 3

=> x = \(\frac{3}{2}\)

h) \(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.....\frac{31}{64}=2^x\)

\(\Rightarrow\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.....\frac{31}{2.32}=2^x\)

\(\Rightarrow\frac{1.2.3.4.....31}{\left(2.2\right).\left(2.3\right).\left(2.4\right).....\left(2.32\right)}=2^x\)

\(\Rightarrow\frac{2.3.4.....31}{2^{31}.32.\left(2.3.4.....31\right)}=2^x\)

\(\Rightarrow\frac{1}{2^{31}.2^5}=2^x\)\(\Rightarrow\frac{1}{2^{36}}=2^x\)

\(\Rightarrow2^x=2^{-36}\Rightarrow x=-36\)

Answer 2

[Lê Minh Thảo]

a)x=4

b)x=0;x=1

c)x=2

d)x=9/2

g)x=-1/2

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