ĐKXĐ: \(x\ge0\)
Ta có;
\(\sqrt{x^2}-2x=5\)
<=> \(\left|x\right|-2x=5\)
<=> \(\left|x\right|=5+2x\)
<=>
* TH1: \(x=5+2x\) <=> \(x=-5\) (loại)
*TH 2: \(x=-5-2x\) <=> \(3x=-5\) \(x=-\frac{5}{3}\) (loại)
Vậy phương trình trên vô nghiệm
tìm x
\(\sqrt{x-2+\sqrt{2x-5}}+\sqrt{x+2+3\sqrt{2x-5}}=\sqrt{\frac{2}{7}}\)
4. Tìm x, biết : ( giải cụ thể nha )
a) \(\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=\sqrt{2}\)
b) \(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=2\sqrt{2}\)
Tìm x: \(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=2\sqrt{2}\)
Tìm `ĐKXĐ`:
\(\sqrt{\dfrac{-5}{6+x}}\)
\(\sqrt{\dfrac{-2}{6-x}}\)
\(\sqrt{\dfrac{-x+3}{-6}}\)
\(\sqrt{\dfrac{7x-1}{-9}}\)
\(\sqrt{\dfrac{x+2}{x^2+2x+1}}\)
\(\sqrt{\dfrac{x-2}{x^2-2x+4}}\)
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) \(\dfrac{1}{\sqrt{-3a}}\)
Tìm x biết
a) \(\sqrt{-x^2+2x-1}=\sqrt{9-12x+4x^2}\)
b) \(\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=2\sqrt{2}\)
c)\(x^2+x+12\sqrt{x+1}=36\)
tìm x để các biểu thức sau có nghĩa:
a)\(\sqrt{\left(x-2\right)}\)+\(\dfrac{1}{x-5}\) b)\(\sqrt{\left(2x-6\right)\left(7-x\right)}\) c)\(\sqrt{4x^2-25}\)
d)\(\dfrac{2}{x^2-9}\)-\(\sqrt{5-2x}\) e)\(\dfrac{x}{x^2-4}\)+\(\sqrt{x-2}\)
Cho B=\(\dfrac{\sqrt{x}-1}{2x+2-2x\sqrt{x}}\)
a)Tính B khi x=\(6+2\sqrt{5}\)
b)tìm x nguyên để b nguyên
Tìm x
a)\(\sqrt{\left(2x-1\right)^2}=x+1\)
b)\(\sqrt{x+3}=5\)
c)\(\sqrt{x+2}=\sqrt{7}\)
Tìm GTLN của biểu thức
a) \(A=\dfrac{1}{x-\sqrt{x}+2}\)
b) \(B=\dfrac{2x-2\sqrt{x}+5}{x-\sqrt{x}+2}\)