8x+3 + 23x - 29 = 218
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a) -8x2+5x+3=-8x^2+8x-3x+3=-8x(x-1)-3(x-1)=-(8x+3)(x-1)
b)8x^2-10x-3=8x^2-12x+2x-3=8x(x-1,5)+2(x-1,5)=2(4x+1)(x-1,5)
c)=8x^2-2x+12x-3=2x(4x-1)+3(4x-1)=(2x+3)(4x-1)
d)=-8x^2+24x-x+3=-8x(x-3)-(x-3)=-(8x+1)(x-3)
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d) \(4x^4-x^2=x^2\left(4x^2-1\right)=x^2\left(2x-1\right)\left(2x+1\right)\)
e) Ta có: \(6x^2-7x-5\)
\(=6x^2-10x+3x-5\)
\(=2x\left(3x-5\right)+\left(3x-5\right)\)
\(=\left(3x-5\right)\left(2x+1\right)\)
f: Ta có: \(-4x^2+23x-15\)
\(=-4x^2+20x+3x-15\)
\(=-4x\left(x-5\right)+3\left(x-5\right)\)
\(=\left(x-5\right)\left(-4x+3\right)\)
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\(\Leftrightarrow x^4-4x^3+4x^2-4x^3+16x^2-16x+3x^2-12x+12\le0\)
\(\Leftrightarrow x^2\left(x^2-4x+4\right)-4x\left(x^2-4x+4\right)+3\left(x^2-4x+4\right)\le0\)
\(\Leftrightarrow\left(x^2-4x+3\right)\left(x-2\right)^2\le0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x^2-4x+3\le0\end{matrix}\right.\) \(\Rightarrow1\le x\le3\)
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\(8x^2-23x-3=8x^2+x-24x-3\)
\(=\left(8x^2+x\right)-\left(24x+3\right)\)
\(=x\left(8x+1\right)-3\left(8x+1\right)\)
\(=\left(8x+1\right)\left(x-3\right)\)
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`#3107.101107`
a)
\(5\left(x-1\right)^3=40\\\Rightarrow\left(x-1\right)^3=40\div5\\ \Rightarrow\left(x-1\right)^3=8\\ \Rightarrow\left(x-1\right)^3=2^3\\ \Rightarrow x-1=2\\ \Rightarrow x=2+1\\ \Rightarrow x=3\)
Vậy, `x = 3`
b)
\(3^{2x+1}+9^x=324?\\ \Rightarrow3^{2x}\cdot3+3^{2x}=324\\ \Rightarrow3^{2x}\cdot\left(3+1\right)=324\\ \Rightarrow3^{2x}\cdot4=324\\ \Rightarrow3^{2x}=81\\ \Rightarrow3^{2x}=3^4\\ \Rightarrow2x=4\\ \Rightarrow x=2\)
Vậy, `x = 2`
c)
\(5^x-13=3\cdot2^2\\ \Rightarrow5^x-13=12\\ \Rightarrow5^x=12+13\\ \Rightarrow5^x=25\\ \Rightarrow5^x=5^2\\ \Rightarrow x=2\)
Vậy, `x = 2`
d)
\(8^x+2^{3x+1}=192\\ \Rightarrow2^{3x}+2^{3x}\cdot2=192\\ \Rightarrow2^{3x}\left(1+2\right)=192\\ \Rightarrow2^{3x}\cdot3=192\\ \Rightarrow2^{3x}=64\\ \Rightarrow2^{3x}=2^6\\ \Rightarrow3x=6\\ \Rightarrow x=2\)
Vậy, `x = 2.`
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8x - 10x - 23x = 25
(8-10-23). x = 25
(-25) . x = 25
x = 25 : (-25)
x = -1
Vậy x =-1
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a) \(=16x^2-56x\)
b) \(=161x^3+184x^2-207x\)
c) \(=7x^3y^2+28x^2y^3-7x^2y^2+7xy^3\)
d) \(=-5x^3+10x^2+5x\)
\(8^{x+3}+2^{3x}-2^9=2^{18}\)
\(2^{3\left(x+3\right)}+2^{3x}-2^9=2^{18}\)
\(2^{3x+9}+2^{3x}=2^{18}+2^9\)
\(2^{3x}\left(2^9+1\right)=2^9\left(2^9+1\right)\)
\(2^{3x}=2^9\)
\(\Rightarrow3x=9\)
\(x=9:3\)
\(x=3\)