`sqrt{4x+20}-3sqrt{5+x}+4/3sqrt{9x+15}=6(x>=-5)`

`<=>sqrt{4(x+5)}-3sqrt{x+5}+4/3sqrt{9(x+5)}=6`

`<=>2sqrt{x+5}-3sqrt{x+5}+4sqrt{x+5}=6`

`<=>3sqrt{x+5}=6`

`<=>sqrt{x+5}=2`

`<=>x+5=4`

`<=>x=-1(tm)`

Vậy `x=-1`

Ta có: \(\sqrt{4x+20}-3\sqrt{x+5}+\dfrac{4}{3}\cdot\sqrt{9x+45}=6\)

\(\Leftrightarrow2\sqrt{x+5}-3\sqrt{x+5}+\dfrac{4}{3}\cdot3\sqrt{x+5}=6\)

\(\Leftrightarrow0\cdot\sqrt{x+5}=6\left(vôlý\right)\)

ĐKXĐ: `x>=0`

`a,3\sqrt(4x)<sqrt9`

`<=>6sqrt(x)<3`

`<=>sqrtx<1/2`

`=>x<1/4` kết hợp với ĐKXĐ có `0<=x<1/2`

KL....

`b, 4\sqrt(8x)>=2`

`<=>\sqrt(8x)>=1/2`

`=>8x>=1/4`

`<=>x>=1/32(TMĐK)`

KL...

a) ĐKXĐ: \(x\ge-4\)

a) Ta có: \(\sqrt{6-4x+x^2}=x+4\Rightarrow\left(x+4\right)^2=x^2-4x+6\)

\(\Rightarrow x^2+8x+16=x^2-4x+6\Rightarrow4x+10=0\Rightarrow x=-\frac{5}{2}\left(loại\right)\)

Vậy pt vô nghiệm

b) \(\sqrt{4x^2-4x+1}+\sqrt{2x-1}=0\Rightarrow\sqrt{\left(2x-1\right)^2}+\sqrt{2x-1}=0\)

\(\Leftrightarrow\sqrt{2x-1}\left(\sqrt{2x-1}+1\right)=0\Rightarrow x=\frac{1}{2}\)

a) Bpt luôn đúng với mọi x không âm

b) đk: \(x\le2\)

Có: \(\sqrt{x}>\sqrt{2-x}\Leftrightarrow x>2-x\)
\(\Leftrightarrow2x>2\Leftrightarrow x>1\)

Kết hợp với đk, ta được: \(1< x\le2\)

\(a,\Leftrightarrow x-1=4\Leftrightarrow x=5\\ b,\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{3}{4}\\3x+1=4x-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ge\dfrac{3}{4}\\x=4\left(tm\right)\end{matrix}\right.\Leftrightarrow x=4\\ c,ĐK:x\ge-5\\ PT\Leftrightarrow2\sqrt{x+5}-3\sqrt{x+5}+4\sqrt{x+5}=6\\ \Leftrightarrow3\sqrt{x+5}=6\\ \Leftrightarrow\sqrt{x+5}=3\\ \Leftrightarrow x+5=9\\ \Leftrightarrow x=4\left(tm\right)\)

\(d,\Leftrightarrow\sqrt{\left(x-2\right)^2}=\sqrt{\left(\sqrt{5}+1\right)^2}\\ \Leftrightarrow\left|x-2\right|=\sqrt{5}+1\\ \Leftrightarrow\left[{}\begin{matrix}x-2=\sqrt{5}+1\\2-x=\sqrt{5}+1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{5}+3\\x=1-\sqrt{5}\end{matrix}\right.\)

Giúp mình với 

a, x = 225

b, x = 49

c, x < 4

\(a.\sqrt{x}=15\)

\(\Leftrightarrow x=15^2=225\)

\(b.2\sqrt{x}=14\)

\(\Leftrightarrow\sqrt{x}=7\)

\(\Leftrightarrow x=7^2=49\)

\(c.22\sqrt{x}< 4\)

\(\Leftrightarrow\sqrt{x}< \dfrac{2}{11}\)

\(\Leftrightarrow x< \left(\dfrac{2}{11}\right)^2\)

\(\Leftrightarrow x< \dfrac{4}{121}\)

a: ĐKXĐ: \(x\in R\)

\(\sqrt{x^2-4x+4}=7\)

=>\(\sqrt{\left(x-2\right)^2}=7\)

=>|x-2|=7

=>\(\left[{}\begin{matrix}x-2=7\\x-2=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=9\\x=-5\end{matrix}\right.\)

b: ĐKXĐ: x>=-3

\(\sqrt{4x+12}-3\sqrt{x+3}+\dfrac{4}{3}\cdot\sqrt{9x+27}=6\)

=>\(2\sqrt{x+3}-3\sqrt{x+3}+\dfrac{4}{3}\cdot3\sqrt{x+3}=6\)

=>\(3\sqrt{x+3}=6\)

=>\(\sqrt{x+3}=2\)

=>x+3=4

=>x=1(nhận)

đặt \(S=\frac{a}{4b^2+1}+\frac{b}{4c^2+1}+\frac{c}{4a^2+1}\)

\(=\frac{a^3}{4a^2b^2+a^2}+\frac{b^3}{4b^2c^2+b^2}+\frac{c^3}{4a^2c^2+c^2}\ge\frac{\left(a\sqrt{a}+b\sqrt{b}+c\sqrt{c}\right)^2}{4a^2b^2+4b^2c^2+4c^2a^2+a^2+b^2+c^2}\)

xét hiệu:

1-4(a²b²+b²c²+c²a²)-a²-b²-c²

=2ab+2bc+2ca-4(a²b²+b²c²+c²a²)

=2ab(1-2ab)+2bc(1-2bc)+2ca(1-2ca)

ta có:

\(2ab\le\frac{\left(a+b\right)^2}{2}\le\frac{1}{2};2bc\le\frac{\left(b+c\right)^2}{2}\le\frac{1}{2};2ca\le\frac{\left(c+a\right)^2}{2}\le\frac{1}{2}\)

\(\Rightarrow2ab\left(1-2ab\right);2bc\left(1-2bc\right);2ca\left(1-2ca\right)\ge0\)

\(\Rightarrow1\ge4\left(a^2b^2+b^2c^2+c^2a^2\right)+a^2+b^2+c^2\)

\(\Rightarrow\frac{\left(a\sqrt{a}+b\sqrt{b}+c\sqrt{c}\right)^2}{4\left(a^2b^2+b^2c^2+c^2a^2\right)+a^2+b^2+c^2}\ge\left(a\sqrt{a}+b\sqrt{b}+c\sqrt{c}\right)^2\)

\(\Rightarrow\frac{a}{4b^2+1}+\frac{b}{4c^2+1}+\frac{c}{4a^2+1}\ge\left(a\sqrt{a}+b\sqrt{b}+c\sqrt{c}\right)^2\)

=>đpcm

dấu"=" xảy ra khi 1 số=1;2 số còn lại =0