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please help me
giúp vs ạ
Bài 2 :
a ) \(\sqrt{4x-8}+\sqrt{x-2}=4+\dfrac{1}{3}\sqrt{9x-18}\) ( ĐKXĐ : \(x\ge2\) )
\(\Leftrightarrow2\sqrt{x-2}+\sqrt{x-2}=4+\dfrac{1}{3}.3\sqrt{x-2}\)
\(\Leftrightarrow3\sqrt{x-2}-\sqrt{x-2}=4\)
\(\Leftrightarrow2\sqrt{x-2}=4\)
\(\Leftrightarrow\sqrt{x-2}=2\)
\(\Leftrightarrow x-2=4\)
\(\Leftrightarrow x=2\) ( thỏa mãn ĐKXĐ )
Vậy phương trình có nghiệm x = 2 .
Bài 2 :
b ) \(\sqrt{x^2-6x+9}-\dfrac{\sqrt{6}+\sqrt{3}}{\sqrt{2}+1}=0\)
\(\Leftrightarrow\sqrt{\left(x-3\right)^2}-\dfrac{\sqrt{3}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}=0\)
\(\Leftrightarrow|x-3|-\sqrt{3}=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3-\sqrt{3}=0\left(x\ge3\right)\\3-x-\sqrt{3}=0\left(x< 3\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3+\sqrt{3}\\x=3-\sqrt{3}\end{matrix}\right.\)
Vậy phương trình cón nghiệm \(x=3+\sqrt{3}\) hoặc \(x=3-\sqrt{3}\) .
D = \(\sqrt{7+\sqrt{33}}+\sqrt{7-\sqrt{33}}\)
=> D2 = \(7+\sqrt{33}+2\left(\sqrt{7+\sqrt{33}}\right)\left(\sqrt{7-\sqrt{33}}\right)+7-\sqrt{33}\)
D2 = \(14+2\left(49-33\right)\) = 14+32 = 48
=> D = \(\sqrt{48}\)
thì e chúc sau
vs
mình câu 8 với ạ
b , Ta có : \(\dfrac{x\sqrt{x}-y\sqrt{y}}{\sqrt{x}-\sqrt{y}}=\dfrac{\left(\sqrt{x}\right)^3-\left(\sqrt{y}\right)^3}{\left(\sqrt{x}-\sqrt{y}\right)}\) = \(\dfrac{\left(\sqrt{x}-\sqrt{y}\right)\left(x+\sqrt{xy}+y\right)}{\sqrt{x}-\sqrt{y}}=x+\sqrt{xy}+y\)
d , Ta có : \(\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\dfrac{1-\sqrt{a}}{1-a}\right)^2=\left(\dfrac{1-a\sqrt{a}+\sqrt{a}-a}{1-\sqrt{a}}\right)\dfrac{\left(1-\sqrt{a}\right)^2}{\left(1-a\right)^2}\)= \(\dfrac{\left(1-a\right)+\sqrt{a}\left(1-a\right)}{1-\sqrt{a}}.\dfrac{\left(1-\sqrt{a}\right)^2}{\left(1-a\right)^2}\)
= \(\dfrac{\left(1-a\right)\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)^2}{\left(1-\sqrt{a}\right)\left(1-a\right)^2}\)
= \(\dfrac{\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)}{\left(1-a\right)}=\dfrac{\left(1-a\right)}{\left(1-a\right)}=1\)
\(2\sqrt{3a}-\sqrt{75a}+\sqrt{\dfrac{13,5}{2a}}-\dfrac{2}{5}\sqrt{300a^3}\left(a>0\right)\)
=\(2\sqrt{3a}-\sqrt{5^2\cdot3a}+a\sqrt{\dfrac{13,5\cdot2a}{\left(2a\right)^2}}-\dfrac{2}{5}\sqrt{10^2\cdot a^2\cdot2}\)
=\(\left(2-5+\dfrac{3}{2}-4a\right)\sqrt{a}\)
=\(\dfrac{-11}{2}a\sqrt{a}\)