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\(2x^2+3\left(x-1\right)\left(x+1\right)=5x\left(x+1\right)\)
\(2x^2+3.\left(x^2-1\right)=5x^2+5x\)
\(2x^2+3x^2-3=5x^2+5x\)
\(5x^2-3=5x^2+5x\)
\(5x=-3\)
\(\Rightarrow x=-\frac{3}{5}\)
Ta có :
\(2x^2+3\left(x-1\right)\left(x+1\right)=5x\left(x+1\right)\)
=> \(2x^2+3\left(x^2-1\right)=5x^2+5x\)
=> \(2x^2+3x^2-3=5x^2+5x\)
=> \(5x^2-3=5x^2+5x\)
=> \(-3=5x\)
=> \(x=-\frac{3}{5}\)
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2.
a) \(x.\left(x^2+x+1\right)-x^2.\left(x+1\right)-x+5\)
\(\Rightarrow x^3+x^2+x-x^3-x^2-x+5\)
\(\Rightarrow\left(x^3-x^3\right)+\left(x^2-x^2\right)+\left(x-x\right)+5\)
\(=5\)( vì kết quả bằng 5 nên đa thức không phụ thuộc vào biến )
b) \(x.\left(2x+1\right)-x^2.\left(x+2\right)+x^3-x+3\)
\(\Rightarrow2x^2+x-x^3-2x^2+x^3-x+3\)
\(\Rightarrow\left(2x^2-2x^2\right)+\left(x-x\right)+\left(-x^3+x^3\right)+3\)
\(=3\)( vì kết quả bằng 3 nên đa thức không phụ thuộc vào biến )
c) \(4.\left(6+x\right)+x^2.\left(2+3x\right)-x.\left(5x+4\right)+3x^2.\left(1-x\right)\)
\(\Rightarrow24+4x+2x^2+3x^3-5x^2+4x+3x^2-3x^3\)
\(\Rightarrow24+\left(4x-4x\right)+\left(2x^2-5x^2+3x^2\right)+\left(3x^3-3x^3\right)\)
\(=24\)( vì kết quả bằng 24 nên đa thức không phụ thuộc vào biến )
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2x^2 + 3.( x^2 - 1^2 ) = 5x^2 + 5x
2x^2 + 3x^2 -3 = 5x^2 + 5x
5x^2 - 5x^2 -3 = 5x
-3 = 5x
x= \(\frac{-3}{5}\)
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\(2x^2+3\left(x-1\right)\left(x+1\right)=5x\left(x+1\right)\)
\(\Leftrightarrow\) \(2x^2+3\left(x^2-1\right)=5x\left(x+1\right)\)
\(\Leftrightarrow\) \(2x^2+3x^2-3=5x^2+5x\)
\(\Leftrightarrow\) \(2x^2+3x^2-5x^2-5x=3\)
\(\Leftrightarrow\) \(-5x=3\)
\(\Leftrightarrow\) \(x=\frac{-3}{5}\)
Vậy ..................................................
\(2x^2+3\left(x-1\right)\left(x+1\right)=5x\left(x+1\right)\)
\(\Leftrightarrow2x^2+3\left(x^2+1\right)-5x^2-5x=0\)
\(\Leftrightarrow5x+3=0\)
\(\Leftrightarrow x=-\frac{3}{5}\)
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\(5x\left(x-3\right)\left(x+3\right)-\left(2x-3\right)^2-5\left(x+2\right)^2\)
\(+34x\left(x+2\right)=1\)
\(\Leftrightarrow5x\left(x^2-9\right)-\left(4x^2-12x+9\right)-5\left(x^2+4x+4\right)\)
\(+34x^2+68x=0\)
\(\Leftrightarrow5x^3-45x-4x^2+12x-9-5x^2-20x-20\)
\(+34x^2+68x=0\)
\(\Leftrightarrow5x^3+25x^2+15x-29=0\)
Giải nghiệm ta được ba nghiệm sau:
\(x_1\approx0,776\)
\(x_2\approx-1,96\)
\(x_3\approx-3,82\)
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a) ( 3x - 1 ) ( 2x + 7 ) - ( x + 1 ) ( 6x + 5 ) = 16
<=> 6x2 + 21x - 2x - 7 - ( 6x2 - 5x + 6x - 5) = 16
<=> 6x2 + 21x - 2x - 7 - ( 6x2 + x - 5 ) = 16
<=> 6x2+ 21x - 2x - 7 - 6x2 -x + 5 = 16
<=> 18x - 2 = 16
<=> 18x = 18
=> x = 1
Vậy....
2x3 + 3(x - 1)(x + 1) = 5x(x + 1)
=> 2x3 + 3(x2 - 1) = 5x(x + 1)
=> 2x3 + 3x2 - 3 = 5x2 + 5
=> 2x3 + 3x2 - 3 - 5x2 - 5 = 0
=> 2x3 - 2x2 - 8 = 0
=> 2(x3 - x2 - 4) = 0
=> x3 - x2 - 4 = 0
=> (x - 2)(x2 + x + 2) = 0
=> x = 2
Vì \(x^2+x+2=\left(x+\frac{1}{2}\right)^2+\frac{7}{4}\ge\frac{7}{4}>0\)
Vậy x = 2
5x(x+1) = 5x2 + 5 :))))))))))?