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mình giúp bài 3 cho
\(\sqrt{25x-125}-3\sqrt{\frac{x-5}{9}}-\frac{1}{3}\sqrt{9x-45}=6\left(ĐKXĐ:x\ge5\right)\)
\(< =>\sqrt{25\left(x-5\right)}-3\sqrt{\frac{x-5}{9}}-\frac{1}{3}\sqrt{9\left(x-5\right)}=6\)
\(< =>\sqrt{25}.\sqrt{x-5}-3\frac{\sqrt{x-5}}{\sqrt{9}}-\frac{1}{3}\sqrt{9}.\sqrt{x-5}=6\)
\(< =>5.\sqrt{x-5}-3.\frac{\sqrt{x-5}}{3}-\frac{1}{3}.3.\sqrt{x-5}=6\)
\(< =>5.\sqrt{x-5}-\sqrt{x-5}-\sqrt{x-5}=6\)
\(< =>3\sqrt{x-5}=6< =>\sqrt{x-5}=2\)
\(< =>x-5=4< =>x=4+5=9\left(tmđk\right)\)
a)\(\left(\frac{\sqrt{x}}{2}-\frac{1}{2\sqrt{2}}\right).\left(\frac{x-\sqrt{x}}{\sqrt{x}+1}-\frac{x+\sqrt{x}}{\sqrt{x}-1}\right)\left(ĐKXĐ:x\ne1;x\ge0\right)\)
\(=\frac{\sqrt{2x}-1}{2\sqrt{2}}.\left(\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}+1}-\frac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}-1}\right)\)
\(=\frac{\sqrt{2x}-1}{2\sqrt{2}}.\left[\frac{\sqrt{x}\left(\sqrt{x}-1\right)^2-\sqrt{x}\left(\sqrt{x}+1\right)^2}{x-1}\right]\)
\(=\frac{\sqrt{2x}-1}{2\sqrt{2}}.\left[\frac{\sqrt{x}.\left[\left(\sqrt{x}-1\right)^2-\left(\sqrt{x}+1\right)^2\right]}{x-1}\right]\)
\(=\frac{\sqrt{2x}-1}{2\sqrt{2}}.\left[\frac{\sqrt{x}\left(\sqrt{x}-1+\sqrt{x}+1\right)\left(\sqrt{x}-1-\sqrt{x}-1\right)}{x-1}\right]\)
\(=\frac{\sqrt{2x}-1}{2\sqrt{2}}.\left[\frac{\sqrt{x}\left(2\sqrt{x}\right)\left(-2\right)}{x-1}\right]\)
\(=\frac{\sqrt{2x}-1}{2\sqrt{2}}.\left[\frac{-4x}{x-1}\right]\)
\(=\frac{-\sqrt{2x}\left(\sqrt{2x}-1\right)}{\left(x-1\right)}\)
\(=\frac{\sqrt{2x}-2x}{\left(x-1\right)}\)
M = \(\frac{2\sqrt{x}-9x}{x-5\sqrt{x}+6}-\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{2\sqrt{x}+1}{3-\sqrt{x}}\)
=\(\frac{2\sqrt{x}-9}{x-5\sqrt{x}+6}-\frac{\left(\sqrt{x}+3\right)\left(3-\sqrt{x}\right)+\left(\sqrt{x}-2\right)\left(2\sqrt{x}+1\right)}{\left(\sqrt{x}-2\right)\left(3-\sqrt{x}\right)}\)
=\(\frac{2\sqrt{x}-9}{x-5\sqrt{x}+6}+\frac{9-x+2x-3\sqrt{x}}{x-5\sqrt{x}+6}\)
=\(\frac{x-\sqrt{x}}{x-5\sqrt{x}+6}\)
a/ \(P=\left(\frac{x-7\sqrt{x}+12}{x-4\sqrt{x}+3}+\frac{1}{\sqrt{x}-1}\right).\frac{\sqrt{x}+3}{\sqrt{x}-3}.\)
\(P=\left(\frac{x-7\sqrt{x}+12}{\left(x-4\sqrt{x}+4\right)-1}+\frac{1}{\sqrt{x}-1}\right).\frac{\sqrt{x}+3}{\sqrt{x}-3}\)
\(P=\left(\frac{x-7\sqrt{x}+12}{\left(\sqrt{x}-2\right)^2-1}+\frac{1}{\sqrt{x}-1}\right).\frac{\sqrt{x}+3}{\sqrt{x}-3}\)
\(P=\left(\frac{x-7\sqrt{x}+12}{\left(\sqrt{x}-2-1\right)\left(\sqrt{x}-2+1\right)}+\frac{1}{\sqrt{x}-1}\right).\frac{\sqrt{x}+3}{\sqrt{x}-3}\)
\(P=\left(\frac{x-7\sqrt{x}+12}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-1\right)}+\frac{1}{\sqrt{x}-1}\right).\frac{\sqrt{x}+3}{\sqrt{x}-3}\)
\(P=\frac{x-7\sqrt{x}+12+\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-1\right)}.\frac{\sqrt{x}+3}{\sqrt{x}-3}\)
\(P=\frac{x-6\sqrt{x}+9}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-1\right)}.\frac{\sqrt{x}+3}{\sqrt{x}-3}\)
\(P=\frac{\left(\sqrt{x}-3\right)^2\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)^2\left(\sqrt{x}-1\right)}\) => \(P=\frac{\sqrt{x}+3}{\sqrt{x}-1}\)
b/ Để P>3/4 => \(P=\frac{\sqrt{x}+3}{\sqrt{x}-1}>\frac{3}{4}\)
+/ TH1: x>1 => \(4\left(\sqrt{x}+3\right)>3\left(\sqrt{x}-1\right)\)
<=> \(\sqrt{x}>-16\) => x>1
+/ TH2: 0<x<1 => \(4\left(\sqrt{x}+3\right)< 3\left(\sqrt{x}-1\right)\) => \(\sqrt{x}< -16\)=> Loại
ĐS: x>1
c/ P=2 <=> \(P=\frac{\sqrt{x}+3}{\sqrt{x}-1}=2\)
<=> \(\sqrt{x}+3=2\left(\sqrt{x}-1\right)\)
<=> \(\sqrt{x}=5=>x=25\)
\(a,x=7-4\sqrt{3}=4-2.2\sqrt{3}+3\) (Thỏa mãn ĐKXĐ)
\(=\left(2-\sqrt{3}\right)^2\)
\(B=\frac{2}{\sqrt{x}-2}=\frac{2}{\sqrt{\left(2-\sqrt{3}\right)^2}-2}\)
\(=\frac{2}{2-\sqrt{3}-2}=-\frac{2\sqrt{3}}{3}\)
\(b,P=\frac{B}{A}=\frac{2}{\sqrt{x}-2}:\left(\frac{\sqrt{x}}{x-4}+\frac{1}{\sqrt{x}-2}\right)\)
\(=\frac{2}{\sqrt{x}-2}:\left(\frac{\sqrt{x}}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}+\frac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right)\)
\(=\frac{2}{\sqrt{x}-2}:\frac{\sqrt{x}+\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\frac{2}{\sqrt{x}-2}:\frac{2\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\frac{2}{\sqrt{x}-2}.\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{2\left(\sqrt{x}+1\right)}\)
\(=\frac{\sqrt{x}+2}{\sqrt{x}+1}\)
\(P=\frac{4}{3}\Rightarrow\frac{\sqrt{x}+2}{\sqrt{x}+1}=\frac{4}{3}\)
\(\Leftrightarrow3\left(\sqrt{x}+2\right)=4\left(\sqrt{x}+1\right)\)
\(\Leftrightarrow3\sqrt{x}+6=4\sqrt{x}+4\)
\(\Leftrightarrow6-4=4\sqrt{x}-3\sqrt{x}\)
\(\Leftrightarrow\sqrt{x}=2\Leftrightarrow x=4\)(ko thỏa mãn ĐKXĐ)
=>pt vo nghiệm
d,\(\left(\sqrt{x}+1\right)P-\sqrt{x}-4\sqrt{x-1}+26=-6x+10\sqrt{5x}\)
\(\Leftrightarrow\left(\sqrt{x}+1\right)\frac{\sqrt{x}+2}{\sqrt{x}+1}-\sqrt{x}-4\sqrt{x-1}+26=-6x+10\sqrt{5x}\)
\(\Leftrightarrow\sqrt{x}+2-\sqrt{x}-4\sqrt{x-1}+26=-6x+10\sqrt{5x}\)
\(\Leftrightarrow-4\sqrt{x-1}+28=-6x+10\sqrt{5x}\)
\(\Leftrightarrow x=5\)
\(P=\left(\frac{3x+3}{x-9}-\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{3-\sqrt{x}}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right).ĐKXĐ:x\ge0,x\ne9\)
\(=\left(\frac{3x+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}-\frac{2\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}-\frac{\sqrt{x}\left(\sqrt{x}+3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right)\)
\(=\left(\frac{3x+3-2x+6\sqrt{x}-x-3\sqrt{x}}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\right):\left(\frac{2\sqrt{x}-2-\sqrt{x}+3}{\sqrt{x}-3}\right)\)
\(=\frac{3\sqrt{x}+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}:\frac{\sqrt{x}+1}{\sqrt{x}-3}\)
\(=\frac{3\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}.\frac{\sqrt{x}-3}{\sqrt{x}+1}\)
\(=\frac{3}{\sqrt{x}+3}\)
\(b,x=20-6\sqrt{11}=11-2.3\sqrt{11}+9\)
\(=\left(\sqrt{11}-3\right)^2\)
\(P=\frac{3}{\sqrt{x}+3}=\frac{3}{\sqrt{\left(\sqrt{11}-3\right)^2}+3}=\frac{3}{\sqrt{11}-3+3}=\frac{3\sqrt{11}}{11}\)
\(c,P>\frac{1}{2}\Rightarrow\frac{3}{\sqrt{x}+3}>\frac{1}{2}\)
\(\Leftrightarrow\frac{3}{\sqrt{x}+3}-\frac{1}{2}>0\)
\(\Leftrightarrow\frac{6-\sqrt{x}-3}{2\left(\sqrt{x}+3\right)}>0\)
\(\Leftrightarrow\frac{6-\sqrt{x}-3}{2\left(\sqrt{x}+3\right)}>0\)\(\Leftrightarrow\frac{3-\sqrt{x}}{2\left(\sqrt{x}+3\right)}>0\)
vì \(2\left(\sqrt{x}+3\right)>0\) (nếu x=0 =>pt vô nghiệm)
\(\Rightarrow3-\sqrt{x}>0\Rightarrow\sqrt{x}< 3\Rightarrow x< 9\)
Kết hợp ĐKXĐ: \(0< x< 9\)