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a/ Theo bài ra: \(x^2+y^2=6;xy=1\)
=> \(x^2+y^2+2xy=8\)
=> \(\left(x+y\right)^2=8\)
=> \(x+y=\sqrt{8}\)
b/ Theo bài ra: \(x^2+y^2=14;xy=1\)
=>\(x^2+y^2-2xy=12\)
=> \(\left(x-y\right)^2=12\)
=> \(x-y=\sqrt{12}\)
c/ Theo bài ra: \(a^2+b^2=116;ab=40\)
=> \(\left(a^2+b^2\right)^2=116^2;a^2b^2=1600\)
=> \(a^4+b^4+2a^2b^2=116^2\)
=> \(a^4-2a^2b^2+b^4+4a^2b^2=13456\)
=> \(a^4-2a^2b^2+b^4=7056\)
\(a,\left|x+3,4\right|+\left|x+2,4\right|+\left|x+7,2\right|=4x\)
\(\left|x+3,4\right|\ge0;\left|x+2,4\right|\ge0;\left|x+7,2\right|\ge0\)
\(< =>\left|x+3,4\right|+\left|x+2,4\right|+\left|x+7,2\right|>0\)
\(< =>4x>0\)
\(x>0\)
\(\hept{\begin{cases}\left|x+3,4\right|=x+3,4\\\left|x+2,4\right|=x+2,4\\\left|x+7,2\right|=x+7,2\end{cases}}\)
\(x+3,4+x+2,4+x+7,2=4x\)
\(x=13\left(TM\right)\)
\(b,3^{n+3}+3^{n+1}+2^{n+3}+2^{n+2}\)
\(3^n.27+3^n.3+2^n.8+2^n.4\)
\(3^n.30+2^n.12\)
\(\hept{\begin{cases}3^n.30⋮6\\2^n.12⋮6\end{cases}}\)
\(< =>3^n.30+2^n.12⋮6< =>VP⋮6\)
Answer:
\(\frac{x+1}{64}+\frac{x+2}{63}+\frac{x+3}{62}+\frac{x+4}{61}=-4\)
\(\Leftrightarrow\frac{x+1}{64}+1+\frac{x+2}{63}+1+\frac{x+3}{62}+1+\frac{x+4}{61}+1=-4+4\)
\(\Leftrightarrow\frac{x+1+64}{64}+\frac{x+2+63}{63}+\frac{x+3+62}{62}+\frac{x+4+61}{61}=0\)
\(\Leftrightarrow\frac{x+65}{64}+\frac{x+65}{63}+\frac{x+65}{62}+\frac{x+65}{61}=0\)
\(\Leftrightarrow\left(x+65\right)\frac{1}{64}+\left(x+65\right)\frac{1}{63}+\left(x+65\right)\frac{1}{62}+\left(x+65\right)\frac{1}{61}=0\)
\(\Leftrightarrow\left(x+65\right)\left(\frac{1}{64}+\frac{1}{63}+\frac{1}{62}+\frac{1}{61}\right)=0\)
\(\Leftrightarrow x+65=0\)
\(\Leftrightarrow x=-65\)