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\(\left(x+4\right)\left(x+6\right)\left(x-2\right)\left(x-12\right)=25x^2\)
\(\Leftrightarrow\left(x+3\right)\left(x+8\right)\left(x^2-15x+24\right)=0\)
\(x^4-8x^3+21x^2-24x+9=0\)
\(\Leftrightarrow\left(x^2-3x+3\right)\left(x^2-5x+3\right)=0\)
\(\Leftrightarrow\left(x-\frac{5+\sqrt{13}}{2}\right)\left(x-\frac{5-\sqrt{13}}{2}\right)=0\) (vì \(x^2-3x+3=\left(x-\frac{3}{2}\right)^2+0,75>0\))
\(\Rightarrow\orbr{\begin{cases}x=\frac{5+\sqrt{13}}{2}\\x=\frac{5-\sqrt{13}}{2}\end{cases}}\)
Ta có
\(x=\frac{\sqrt{4+2\sqrt{3}}-\sqrt{3}}{\left(\sqrt{5}+2\right)\sqrt[3]{17\sqrt{5}-38}-2}\)
\(=\frac{\sqrt{3+2\sqrt{3}+1}-\sqrt{3}}{\left(\sqrt{5}+2\right)\sqrt[3]{5\sqrt{5}-3.5.2+3.4.\sqrt{5}-8}-2}\)
\(=\frac{\sqrt{3}+1-\sqrt{3}}{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)-2}=\frac{1}{5-4-2}=-1\)
Thế vào ta được
\(P=\left(x^2+x+1\right)^{2013}+\left(x^2+x-1\right)^{2013}\)
\(=\left(1-1+1\right)^{2013}+\left(1-1-1\right)^{2013}=1-1=0\)
\(a,\Delta=4\left(m-1\right)^2-4\left(-2m-3\right)=4m^2-8m+4+8m+12\\ \Delta=4m^2+16>0\left(đpcm\right)\\ b,\Delta=\left(2m-1\right)^2-4\left(2m-2\right)=4m^2-4m+1-8m+8\\ \Delta=4m^2-12m+9=\left(2m-3\right)^2\ge0\left(đpcm\right)\\ c,Sửa:x^2-2\left(m+1\right)x+2m-2=0\\ \Delta=4\left(m+1\right)^2-4\left(2m-2\right)=4m^2+8m+4-8m+8\\ \Delta=4m^2+12>0\left(đpcm\right)\\ d,\Delta=4\left(m+1\right)^2-4\cdot2m=4m^2+8m+4-8m\\ \Delta=4m^2+4>0\left(đpcm\right)\\ e,\Delta=4m^2-4\left(m+7\right)=4m^2-4m+7=\left(2m-1\right)^2+6>0\left(đpcm\right)\\ f,\Delta=4\left(m-1\right)^2-4\left(-3-m\right)=4m^2-8m+4+12+4m\\ \Delta=4m^2-4m+16=\left(2m-1\right)^2+15>0\left(đpcm\right)\)
a,ĐKXĐ:\(x\ge2\)
\(4\sqrt{x-2}+\sqrt{9x-18}-\sqrt{\dfrac{x-2}{4}}=26\\ \Leftrightarrow4\sqrt{x-2}+3\sqrt{x-2}-\dfrac{\sqrt{x-2}}{2}=26\\ \Leftrightarrow8\sqrt{x-2}+6\sqrt{x-2}-\sqrt{x-2}=52\\ \Leftrightarrow13\sqrt{x-2}=52\\ \Leftrightarrow\sqrt{x-2}=4\\ \Leftrightarrow x-2=16\\ \Leftrightarrow x=18\left(tm\right)\)
b,ĐKXĐ:\(x\in R\)
\(3x+\sqrt{4x^2-8x+4}=1\\ \Leftrightarrow2\sqrt{x^2-2x+1}=1-3x\\ \Leftrightarrow\left|x-1\right|=\dfrac{1-3x}{2}\\ \Leftrightarrow\left[{}\begin{matrix}x-1=\dfrac{1-3x}{2}\\x-1=\dfrac{3x-1}{2}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x-2=1-3x\\2x-2=3x-1\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{5}\left(tm\right)\\x=-1\left(tm\right)\end{matrix}\right.\)
c, ĐKXĐ:\(x\ge0\)
\(\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)=7\\ \Leftrightarrow\sqrt{x}\left(2\sqrt{x}+1\right)-2\left(2\sqrt{x}+1\right)=7\\ \Leftrightarrow2x+\sqrt{x}-4\sqrt{x}-2=7\\ \Leftrightarrow2x-3\sqrt{x}-9=0\\ \Leftrightarrow\left(2x+3\sqrt{x}\right)-\left(6\sqrt{x}+9\right)=0\\ \Leftrightarrow\sqrt{x}\left(2\sqrt{x}+3\right)-3\left(2\sqrt{x}+3\right)=0\\ \Leftrightarrow\left(\sqrt{x}-3\right)\left(2\sqrt{x}+3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=3\\2\sqrt{x}=-3\left(vô.lí\right)\end{matrix}\right.\\ \Leftrightarrow x=9\left(tm\right)\)
\(\hept{\begin{cases}\left(x+1\right)\left(2y+3\right)=5\\\left(x+2\right)\left(3y-1\right)=-4\end{cases}\Rightarrow x+1=\frac{5}{2y+3}\Leftrightarrow x+2=\frac{8+2y}{2y+3}}\)
\(\Leftrightarrow\left(x+2\right)\left(3y-1\right)=\left(\frac{8+2y}{2y+3}\right)\left(3y-1\right)=-4\)
\(\Leftrightarrow\left(8+2y\right)\left(3y-1\right)=-8y-12\\ \Leftrightarrow6y^2+30y+4=0\)
\(\Rightarrow\orbr{\begin{cases}y=\frac{-15+\sqrt{201}}{6}\\y=\frac{-15-\sqrt{201}}{6}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{-83-5\sqrt{201}}{8}\\x=\frac{-83+5\sqrt{201}}{8}\end{cases}}\)
cảm ơn nha! mk bt cách làm rùi nhưng mà bạn tính x sai mất rùi! dù sao cũng camon nhìu lắm!!! ^ ^
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+y+1\right)\left(x+y-6\right)=0\\y-x-3=0\left(3\right)\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=-\left(y+1\right)\left(1\right)\\x=6-y\left(2\right)\end{matrix}\right.\\y-x-3=0\left(3\right)\end{matrix}\right.\)
\(thế\left(1\right)\left(2\right)vào\left(3\right)\Rightarrow\left(x;y\right)\)
1)x^4+x^2-6x+1=0>>>x^4+4x^2+4-3x^2-6x-3=0>>>(x^2+2)^2=3(x-1)^2.
>>Sau đó giải bt.
2)Đặt x^2-x+1=a;x+1=b thì:x^3+1=ab.
Pt:2a+5b^2+14ab=0(tự giải nha)