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a: \(=2\sqrt{x-3}+3\sqrt{x-3}-4\sqrt{x-3}+3-x\)
\(=\sqrt{x-3}+3-x\)
c: \(\Leftrightarrow7\sqrt{x-2}-2\sqrt{x-2}-3\sqrt{x-2}=18\)
=>2 căn x-2=18
=>x-2=81
=>x=83
a) \(\sqrt{25x+75}+3\sqrt{x-2}=2+4\sqrt{x+3}+\sqrt{9x-18}\) (ĐKXĐ : \(x\ge2\) )
\(\Leftrightarrow5\sqrt{x+3}+3\sqrt{x-2}-4\sqrt{x+3}-3\sqrt{x-2}=2\)
\(\Leftrightarrow\sqrt{x+3}=2\)
\(\Leftrightarrow x+3=4\)
\(\Leftrightarrow x=1\) ( Thỏa mãn ĐKXĐ )
c) \(\sqrt{4x+20}+\sqrt{x+5}-\dfrac{1}{3}\sqrt{9x+45}=4\) (ĐKXĐ : \(x\ge-5\) )
\(\Leftrightarrow2\sqrt{x+5}+\sqrt{x+5}-\sqrt{x+5}=4\)
\(\Leftrightarrow2\sqrt{x+5}=4\)
\(\Leftrightarrow\sqrt{x+5}=2\)
\(\Leftrightarrow x+5=4\)
\(\Leftrightarrow x=-1\) ( Thỏa mãn ĐKXĐ )
Vậy.......
1: =>|2x-1|=5
=>2x-1=5 hoặc 2x-1=-5
=>2x=6 hoặc 2x=-4
=>x=3 hoặc x=-2
2: \(\Leftrightarrow2\sqrt{x-3}+\dfrac{1}{3}\cdot3\sqrt{x-3}-\sqrt{x-3}=4\)
\(\Leftrightarrow\sqrt{x-3}=2\)
=>x-3=4
hay x=7
5: \(\Leftrightarrow\sqrt{x-2}\left(\sqrt{x+2}-1\right)=0\)
=>x-2=0 hoặc x+2=1
=>x=2 hoặc x=-1
Đk:x-3\(\ge\)0
<=>x\(\le\)3
\(\sqrt{4x-12}+\sqrt{9x-27}-4\sqrt{x-3}+3-x=0\)
\(\Leftrightarrow\sqrt{4\left(x-3\right)}+\sqrt{9\left(x-3\right)}-4\sqrt{x-3}-\left(\sqrt{x-3}^2\right)=0\)
\(\Leftrightarrow2\sqrt{\left(x-3\right)}+3\sqrt{\left(x-3\right)}-4\sqrt{x-3}-\left(\sqrt{x-3}^2\right)=0\)
\(\Leftrightarrow\sqrt{x-3}\left(2+3-4-\sqrt{x-3}\right)=0\)
\(\Leftrightarrow\sqrt{x-3}\left(1-\sqrt{x-3}\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}\sqrt{x-3}=0\\1-\sqrt{x-3}=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=3\\x=4\end{cases}}}\)(thõa mãn ĐK)
\(\sqrt{16x+16}-\sqrt{9x+9}+\sqrt{4x+4}+\sqrt{x+1}=16\)
\(\Leftrightarrow4\sqrt{x+1}-3\sqrt{x+1}+2\sqrt{x+1}+\sqrt{x+1}=16\)
\(\Leftrightarrow4\sqrt{x+1}=16\)
\(\Leftrightarrow\sqrt{x+1}=4\)
<=> x + 1 = 16
<=> x = 15 (nhận)
~ ~ ~
\(\sqrt{4x+20}-3\sqrt{5+x}+\dfrac{4}{3}\sqrt{9x+45}=6\)
\(\Leftrightarrow2\sqrt{x+5}-3\sqrt{x+5}+4\sqrt{x+5}=6\)
\(\Leftrightarrow3\sqrt{x+5}=6\)
\(\Leftrightarrow\sqrt{x+5}=2\)
<=> x + 5 = 4
<=> x = - 1 (nhận)
a) x=49
b) x=4
c) x = 2 hoặc x = -2
d) x= 11,17355372
e) x =10
f) x=2
g)x = 10 000 000 ( nếu theo đề của bạn) và x=0,94 ( nếu theo đề bđ)
h) x =4
k) x = 4/3 hoặc x = -2/3
l) x = 2,5
m) x = 0,5
n) x=-0,5
\(\sqrt{25x+75}+3\sqrt{x-2}-2+4\sqrt{x+3}\)\(+\sqrt{9x-18}\)
= \(5\sqrt{x+3}+3\sqrt{x-2}-2+4\sqrt{x+3}+3\sqrt{x-2}\)
= \(9\sqrt{x+3}+6\sqrt{x-2}-2\)
\(\sqrt{4x-12}-\sqrt{9x-27}+\sqrt{\dfrac{25x-75}{4}}-3=0\left(dkxd:x\ge3\right)\)
\(\Leftrightarrow\sqrt{4\left(x-3\right)}-\sqrt{9\left(x-3\right)}+\sqrt{\dfrac{25}{4}\cdot\left(x-3\right)}=3\)
\(\Leftrightarrow2\sqrt{x-3}-3\sqrt{x-3}+\dfrac{5}{2}\sqrt{x-3}=3\)
\(\Leftrightarrow\dfrac{3}{2}\sqrt{x-3}=3\)
\(\Leftrightarrow\sqrt{x-3}=2\)
\(\Leftrightarrow x-3=4\)
\(\Leftrightarrow x=7\left(tmdk\right)\)
Vậy $x=7$.
$Toru$