Giải giúp em câu b bài 2 với ạ
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\(b,B=\dfrac{\sqrt{x}+2}{\sqrt{x}-3}+\dfrac{\sqrt{x}-8}{x-5\sqrt{x}+6}\left(x\ge0;x\ne4;x\ne9\right)\\ B=\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)+\sqrt{x}-8}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\\ B=\dfrac{x-4+\sqrt{x}-8}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}=\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}-4\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}=\dfrac{\sqrt{x}-4}{\sqrt{x}-2}\)
\(c,B< A\Leftrightarrow\dfrac{\sqrt{x}-4}{\sqrt{x}-2}< \dfrac{\sqrt{x}+1}{\sqrt{x}-2}\Leftrightarrow\dfrac{\sqrt{x}-4}{\sqrt{x}-2}-\dfrac{\sqrt{x}+1}{\sqrt{x}-2}< 0\\ \Leftrightarrow\dfrac{-5}{\sqrt{x}-2}< 0\Leftrightarrow\sqrt{x}-2>0\left(-5< 0\right)\\ \Leftrightarrow x>4\\ d,P=\dfrac{B}{A}=\dfrac{\sqrt{x}-4}{\sqrt{x}-2}:\dfrac{\sqrt{x}+1}{\sqrt{x}-2}=\dfrac{\sqrt{x}-4}{\sqrt{x}+1}=1-\dfrac{5}{\sqrt{x}+1}\in Z\\ \Leftrightarrow5⋮\sqrt{x}+1\Leftrightarrow\sqrt{x}+1\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\\ \Leftrightarrow\sqrt{x}\in\left\{-6;-2;0;4\right\}\\ \Leftrightarrow x\in\left\{0;16\right\}\left(\sqrt{x}\ge0\right)\)
\(e,P=1-\dfrac{5}{\sqrt{x}+1}\)
Ta có \(\sqrt{x}+1\ge1,\forall x\Leftrightarrow\dfrac{5}{\sqrt{x}+1}\ge5\Leftrightarrow1-\dfrac{5}{\sqrt{x}+1}\le-4\)
\(P_{max}=-4\Leftrightarrow x=0\)
j, ĐK: \(x\ne\dfrac{\pi}{6}+\dfrac{k\pi}{2}\)
\(tan\left(\dfrac{\pi}{3}+x\right)-tan\left(\dfrac{\pi}{6}+2x\right)=0\)
\(\Leftrightarrow tan\left(\dfrac{\pi}{3}+x\right)=tan\left(\dfrac{\pi}{6}+2x\right)\)
\(\Leftrightarrow\dfrac{\pi}{3}+x=\dfrac{\pi}{6}+2x+k\pi\)
\(\Leftrightarrow x=\dfrac{\pi}{6}+k\pi\left(l\right)\)
\(\Rightarrow\) vô nghiệm.
a, \(u_n=u_1.q^{n-1}\)
\(\Leftrightarrow192=u_1.2^n\)
\(\Leftrightarrow u_1=\dfrac{192}{2^n}\)
\(S_n=\dfrac{u_1\left(1-q^n\right)}{1-q}\)
\(\Leftrightarrow189=\dfrac{\dfrac{192}{2^n}\left(1-2^n\right)}{1-2}\)
\(\Leftrightarrow189=192-\dfrac{192}{2^n}\)
\(\Leftrightarrow\dfrac{192}{2^n}=3\)
\(\Leftrightarrow2^n=2^6\)
\(\Rightarrow n=6\)
\(\Delta'=4-\left(m-1\right)=5-m\)
để pt có nghiệm kép khi \(5-m=0\Leftrightarrow m=5\)
chọn B
Phương trình có nghiệm kép khi:
\(\Delta'=4-\left(m-1\right)=0\Leftrightarrow5-m=0\)
\(\Rightarrow m=5\)
43.a) \(m_{HCl\left(bđ\right)}=200.10,95\%=21,9\left(g\right)\)
=> \(n_{HCl\left(bđ\right)}=\dfrac{21,9}{36,5}=0,6\left(mol\right)\)
b) HCl phản ứng với NaOH là HCl dư
\(HCl+NaOH\rightarrow NaCl+H_2O\)
\(n_{HCl\left(dư\right)}=n_{NaOH}=0,05.2=0,1\left(mol\right)\)
=> \(n_{HCl\left(pứ\right)}=n_{HCl\left(bđ\right)}-n_{HCl\left(dư\right)}=0,6-0,1=0,5\left(mol\right)\)
c) \(CaCO_3+2HCl\rightarrow CaCl_2+H_2O+CO_2\)
\(n_{CaCO_3}=\dfrac{1}{2}n_{HCl\left(pứ\right)}=0,25\left(mol\right)\)
=> \(m_{CaCO_3}=0,25.100=25\left(g\right)\)
d) \(n_{CO_2}=\dfrac{1}{2}n_{HCl\left(pứ\right)}=0,25\left(mol\right)\)
=> \(V_{CO_2}=0,25.22,4=5,6\left(l\right)\)
e) \(m_{ddsaupu}=25+200-0,25.44=214\left(g\right)\)
Dung dịch A gồm CaCl2 và HCl dư
\(n_{CaCl_2}=\dfrac{1}{2}n_{HCl\left(pứ\right)}=0,25\left(mol\right)\)
\(C\%_{CaCl_2}=\dfrac{0,25.111}{214}.100=12,97\%\)
\(C\%_{HCl\left(dư\right)}=\dfrac{0,1.36,5}{214}.100=1,71\%\)
b: Xét ΔABD và ΔBAC có
BA chung
BD=AC
AD=BC
Do đó: ΔABD=ΔBAC
c: ta có: EA+EC=AC
EB+ED=BD
mà AC=BD
và EA=EB
nên EC=ED