tìm x
(7x-3)2011=(3-7x)2010
(3x-1)2=(3x-1)
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a) \(\left(3x-2\right)\left(3x-1\right)=\left(3x+1\right)^2\)
<=> \(9x^2-9x+2=9x^2+6x+1\)
<=> \(15x=1\) <=> \(x=\frac{1}{15}\)
b) \(\left(4x-1\right)\left(x+1\right)=\left(2x-3\right)^2\)
<=> \(4x^2+3x-1=4x^2-12x+9\)
<=> \(15x^2=10\) <=> \(x=\frac{2}{3}\)
c) \(\left(5x+1\right)^2=\left(7x-3\right)\left(7x+2\right)\) <=> \(25x^2+10x+1=49x^2-7x-6\)
<=> \(24x^2-17x-7=0\) <=> \(24x^2-24x+7x-7=0\)
<=> \(\left(24x+7\right)\left(x-1\right)=0\) <=> \(\orbr{\begin{cases}x=-\frac{7}{24}\\x=1\end{cases}}\)
d) (4 - 3x)(4 + 3x) = (9x - 3)(1 - x)
<=> 16 - 9x2 = 12x - 9x2 - 3
<=> 12x = 19
<=> x = 19/12
e) x(x + 1)(x + 2)(x + 3) = 24
<=> (x2 + 3x)(x2 + 3x + 2) = 24
<=> (x2 + 3x)2 + 2(x2 + 3x) - 24 = 0
<=> (x2 + 3x)2 + 6(x2 + 3x) - 4(x2 + 3x) - 24 = 0
<=> (x2 + 3x + 6)(x2 + 3x - 4) = 0
<=> \(\orbr{\begin{cases}x^2+3x+6=0\\x^2+3x-4=0\end{cases}}\)
<=> \(\orbr{\begin{cases}\left(x+\frac{3}{2}\right)^2+\frac{15}{4}=0\left(vn\right)\\\left(x+4\right)\left(x-1\right)=0\end{cases}}\)
<=> \(\orbr{\begin{cases}x=-4\\x=1\end{cases}}\)
g) (7x - 2)2 = (7x - 3)(7x + 2)
<=> 49x2 - 28x + 4 = 49x2 - 7x - 6
<=> 21x = 10 <=> x = 10/21
a, \((\frac{3}{7}-\frac{2}{3})\) .x =\(\frac{10}{21}\)
\(\frac{-5}{21}\).x=\(\frac{10}{21}\)
x= -2
Mk chỉ làm 1 phần các phằn còn lại tương tự
\(pt\Leftrightarrow x^3+3x^2-7x-1+\left(3x+1\right)\sqrt{x^3-7x+6}=0\)
\(\Leftrightarrow\left(x^3+3x^2-7x-1+\left(3x+1\right)\sqrt{x^3-7x+6}\right)\left(x^3+3x^2-7x-1-\left(3x+1\right)\sqrt{x^3-7x+6}\right)=0\)
\(\Leftrightarrow\left(\left(x^3+3x^2-7x-1\right)^2-\left(3x+1\right)^2\left(x^3-7x+6\right)=0\right)\)
Sau đó em giải tiếp đc r ^^ Phá bình phương rồi đặt nhân tử chung.
\(\Rightarrow7x^3+7x^2-4x^2-4x+x+1=0\\ \Rightarrow\left(x+1\right)\left(7x^2-4x+1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-1\\7x^2-4x+1=0\left(1\right)\end{matrix}\right.\\ \left(1\right)\Rightarrow7\left(x^2-2\cdot\dfrac{2}{7}x+\dfrac{4}{49}\right)+\dfrac{3}{7}=0\\ \Rightarrow7\left(x-\dfrac{2}{7}\right)^2+\dfrac{3}{7}=0\left(\text{vô lí}\right)\)
Vậy x=-1
a: \(\Leftrightarrow9x^2-9x+2=9x^2+6x+1\)
=>-3x=-1
hay x=1/3
b: \(\Leftrightarrow4x^2+4x-x-1=4x^2-12x+9\)
=>3x-1=-12x+9
=>15x=10
hay x=2/3
c: \(\Leftrightarrow25x^2+10x+1=25x^2+25x-x-1=24x-1\)
=>10x-24x=-1-1
=>-14x=-2
hay x=1/7
d: \(\Leftrightarrow49x^2-28x+4=49x^2+14x-21x-6\)
=>-28x+4=-7x-6
=>-21x=-10
hay x=10/21