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\(a,\left|x+3,4\right|+\left|x+2,4\right|+\left|x+7,2\right|=4x\)
\(\left|x+3,4\right|\ge0;\left|x+2,4\right|\ge0;\left|x+7,2\right|\ge0\)
\(< =>\left|x+3,4\right|+\left|x+2,4\right|+\left|x+7,2\right|>0\)
\(< =>4x>0\)
\(x>0\)
\(\hept{\begin{cases}\left|x+3,4\right|=x+3,4\\\left|x+2,4\right|=x+2,4\\\left|x+7,2\right|=x+7,2\end{cases}}\)
\(x+3,4+x+2,4+x+7,2=4x\)
\(x=13\left(TM\right)\)
\(b,3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\)
\(3^n.27+3^n.3+2^n.8+2^n.4\)
\(3^n.30+2^n.12\)
\(\hept{\begin{cases}3^n.30⋮6\\2^n.12⋮6\end{cases}}\)
\(< =>3^n.30+2^n.12⋮6< =>VP⋮6\)
ta có: \(\dfrac{3x-4}{y+15}=\dfrac{1}{9}\)
theo đề bài, ta có phương trình:
\(\dfrac{3x-4}{12+15}=\dfrac{1}{9}\)
\(\Rightarrow x=\dfrac{7}{3}\)
Theo bài ra ,ta có :
\(\frac{148-x}{25}+\frac{169-x}{23}+\frac{186-x}{21}+\frac{199-x}{19}=10\)
\(\Leftrightarrow\frac{148-x}{25}-1+\frac{169-x}{23}-2+\frac{186-x}{21}-3+\frac{199-x}{19}-4=0\)
\(\Leftrightarrow\frac{148-25-x}{25}+\frac{169-46-x}{23}+\frac{186-63-x}{21}+\frac{199-76-x}{19}=0\)
\(\Leftrightarrow\frac{123-x}{25}+\frac{123-x}{23}+\frac{123-x}{21}+\frac{123-x}{19}=0\)
\(\Leftrightarrow\left(123-x\right)\left(\frac{1}{25}+\frac{1}{23}+\frac{1}{21}+\frac{1}{19}\right)=0\)
\(\Leftrightarrow123-x=0\)(Vì \(\Leftrightarrow\frac{1}{25}+\frac{1}{23}+\frac{1}{21}+\frac{1}{19}>0\))
\(\Leftrightarrow x=123\)
Vậy x = 123
Chúc bạn học tốt =))
a) \(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)=\left[\left(x+2\right)\left(x+8\right)\right]\left[\left(x+4\right)\left(x+6\right)\right]+16\)
\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+16\)
\(=\left(x^2+10x+20-4\right)\left(x^2+10x+20+4\right)+16\)
\(=\left(x^2+10x+20\right)^2-4^2+16\)
\(=\left(x^2+10x+20\right)^2\)
b) \(x\left(x-1\right)\left(x+1\right)\left(x+2\right)-3\)
\(=\left[x\left(x+1\right)\right]\left[\left(x-1\right)\left(x+2\right)\right]-3\)
\(=\left(x^2+x\right)\left(x^2+x-2\right)-3\)
\(=\left(x^2+x-1+1\right)\left(x^2+x-1-1\right)-3\)
\(=\left(x^2+x-1\right)^2-1^2-3\)
\(=\left(x^2+x-1\right)^2-2^2\)
\(=\left(x^2+x-3\right)\left(x^2+x+1\right)\)
c) \(\left(2x-1\right)\left(x-1\right)\left(x-3\right)\left(2x+3\right)+9\)
\(=\left(2x^2-3x+1\right)\left(2x^2-3x-9\right)+9\)
\(=\left(2x^2-3x-4+5\right)\left(2x^2-3x-4-5\right)+9\)
\(=\left(2x^2-3x-4\right)^2-5^2+9\)
\(=\left(2x^2-3x-4\right)-4^2\)
\(=\left(2x^2-3x\right)\left(2x^2-3x-8\right)\)
\(=x\left(2x-3\right)\left(2x^2-3x-8\right)\)