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a) (2010 - x)(x + 2021) = 0
<=> \(\left[{}\begin{matrix}2010-x=0\\x+2021=0\end{matrix}\right.\)<=> \(\left[{}\begin{matrix}x=2010\\x=-2021\end{matrix}\right.\)
b) (x - 2)^2 + 5(x - 2) = 0
<=> x^2 - 4x + 4 + 5x - 10 = 0
<=> x^2 + x - 6 = 0
<=> x^2 - 2x + 3x - 6 = 0
<=> x(x - 2) + 3(x - 2) = 0
<=> (x + 3)(x - 2) = 0
<=> \(\left[{}\begin{matrix}x+3=0\\x-2=0\end{matrix}\right.\) <=> \(\left[{}\begin{matrix}x=-3\\x=2\end{matrix}\right.\)
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a)
\(\left(2x-15\right)^5=\left(2x-15\right)^3\\ \Leftrightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\\ \Leftrightarrow\left(2x-15\right)^3.\left[\left(2x-15\right)^2-1\right]=0\\ \Leftrightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15-1\right).\left(2d-15+1\right)=0\end{matrix}\right.\\\Leftrightarrow\left[{}\begin{matrix}2x-15=0\\2x-16=0\\2x-14=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=8\\x=7\end{matrix}\right. \)
b) \(\left(7x-11\right)^3=\left(-3\right)^2.15+208\\ \Leftrightarrow\left(7x-11\right)^3=343=7^3\\ \Leftrightarrow7x-11=7\\ \Leftrightarrow x=\dfrac{18}{7}\)
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( 7x - 11 ) 3 = ( -3 )2 .15 + 208
( 7x - 11 ) 3 = 9 .15 + 208
( 7x - 11 ) 3 = 135 + 208
( 7x - 11 ) 3 = 343
( 7x - 11 ) 3 = 73
=> 7x - 11 = 7
=> 7x = 7 + 11 = 18
=> x = 18/7
\(\left(7x-11\right)^3=\left(-3\right)^2.15+208\)
\(\Leftrightarrow\)\(\left(7x-11\right)^3=9.15+208\)
\(\Leftrightarrow\)\(\left(7x-11\right)^3=135+208\)
\(\Leftrightarrow\)\(\left(7x-11\right)^3=343\)
\(\Leftrightarrow\)\(\left(7x-11\right)^3=7^3\)
\(\Leftrightarrow\)\(7x-11=7\)
\(\Leftrightarrow\)\(7x=18\)
\(\Leftrightarrow\)\(x=\frac{18}{7}\)
Vậy \(x=\frac{18}{7}\)
Chúc bạn học tốt ~
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mình sửa lại nha, nãy mình nhìn nhầm dấu:
343x3 - 1617x2 + 2541x - 1674 = 0
x = 18/7 là nghiệm duy nhất của phương trình đã cho