\(\Leftrightarrow\sqrt{2x-3}=x-3\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2-6x+9=2x-3\\x\ge3\end{matrix}\right.\Leftrightarrow x=6\)
Cho :
A =\(\sqrt{\dfrac{2x+3}{x-3}}\) , B = \(\dfrac{\sqrt{2x+3}}{\sqrt{x-3}}\)
a) Tìm x để A có nghĩa
b) Tìm x để B có nghĩa
c) Tìm x để A = B
Tìm điều kiện có nghĩa:
1) \(\sqrt{2x^2}\)
2) \(\sqrt{-x}\)
3) \(\sqrt{-x^2-3}\)
4) \(\sqrt{x^2+2x+3}\)
5) \(\sqrt{-a^2+8a-16}\)
6) \(\sqrt[]{16x^2-25}\)
7) \(\sqrt{4x^2-49}\)
8) \(\sqrt{8-x^2}\)
9) \(\sqrt{x^2-12}\)
10) \(\sqrt{x^2+2x-3}\)
11) \(\sqrt{2x^2+5x+3}\)
12) \(\sqrt{\dfrac{4}{x-1}}\)
13) \(\sqrt{\dfrac{-1}{x-3}}\)
14) \(\sqrt{\dfrac{-3}{x+2}}\)
15) \(\sqrt{\dfrac{1}{2a-1}}\)
16) \(\sqrt{\dfrac{2}{3-2a}}\)
17) \(\sqrt{\dfrac{-1}{2a-5}}\)
18) \(\sqrt{\dfrac{-2}{3-5a}}\)
19) \(\sqrt{\dfrac{-a}{5}}\)
20) \(\dfrac{1}{\sqrt{-3a}}\)
Cho x là số thực. Tìm GTNN:
\(P=\frac{\sqrt{3\left(2x^2+2x+1\right)}}{3}+\frac{1}{\sqrt{2x^2+\left(3-\sqrt{3}\right)x+3}}+\frac{1}{\sqrt{2x^2+\left(3+\sqrt{3}\right)x+3}}\)
Tìm ĐKXĐ:
a) \(\sqrt{72x}\)
b) \(\dfrac{2x+3}{\sqrt{x^2-4}}\)
c) \(\sqrt{\left(2x+1\right)\left(x+2\right)}\)
d) \(3-\sqrt{16x^2-1}\)
e) \(\sqrt{\dfrac{3+x}{4-x}}\)
Tìm điều kiện có nghĩa:
1) \(\sqrt{x^2+2x-3}\)
2) \(\sqrt{2x^2+5x+3}\)
3) \(\sqrt{\dfrac{4}{x-1}}\)
4) \(\sqrt{\dfrac{-1}{x-3}}\)
5) \(\sqrt{\dfrac{-3}{x+2}}\)
6) \(\sqrt{\dfrac{1}{2a-1}}\)
LÀM CHI TIẾT GIÚP MK NHÉ!
3) tìm x biết
a) \(\sqrt{x+9}=7\)
b) \(4\sqrt{2x+3}-\sqrt{8x+12}+\dfrac{1}{3}\sqrt{18x+27}=15\)
c) \(\sqrt{x^2-6x+9}=2x+1\)
d) \(\sqrt{x+3+4\sqrt{x-1}}-\sqrt{x+8+6\sqrt{x-1}}=9\)
lm nhanh giúp mk nhé mk đang cần gấp
A=\(\dfrac{\sqrt{x}+1}{2\sqrt{x}-1}+\dfrac{\sqrt{x}}{\sqrt{x}+3}-\dfrac{x+6\sqrt{x}+2}{2x+5\sqrt{x}-3}\) B=\(\dfrac{\sqrt{x}+3}{x+8}\) Tìm GTLN: P=AB
tìm x thoả mãn
\(\left(x+2\right)\left(\sqrt{2x+3}+\sqrt{x+1}\right)+\sqrt{2x^2+5x+3}=1\left(với:x\ge-1\right)\)
Tìm x không am biết
a) \(\sqrt{x}\)=21
b) 3\(\sqrt{x}\)=18
c) \(\sqrt{x}\) < hoặc = \(\sqrt{5}\)
d) 3\(\sqrt{2x}\)>9
Tìm điều kiện để các biểu thức sau xác định
a)\(\sqrt{x+1}-\dfrac{1}{2}\)
b)\(2.\sqrt{1-2x}-\dfrac{\sqrt{3}-1}{4}\)
c)\(\sqrt{x+1}-\sqrt{x-2}\)
d)\(\sqrt{2-3x}-\sqrt{1-2x}\)
e)\(2.\sqrt{\sqrt{3}-2x}+\dfrac{1}{x-1}\)
f)\(\dfrac{1}{2}.\sqrt{x-\dfrac{\sqrt{3}}{2}}-\dfrac{1}{\sqrt{x}-1}\)
g)\(\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}+2}\)
h)\(\dfrac{1}{\sqrt{x}+1}-\dfrac{1}{\sqrt{x^2+2}}\)
