`(4\sqrt{6}+x)^2=8^2+(6+\sqrt{x^2+4})^2`

`<=>96+8\sqrt{6}x+x^2=64+36+12\sqrt{x^2+4}+x^2+4`

`<=>2\sqrt{6}x-2=3\sqrt{x^2+4}`    `ĐK: x >= \sqrt{6}/6`

`<=>24x^2-8\sqrt{6}x+4=9x^2+36`

`<=>15x^2-8\sqrt{6}x-32=0`

`<=>x^2-[8\sqrt{6}]/15x-32/15=0`

`<=>(x-[4\sqrt{6}]/15)^2-64/25=0`

`<=>|x-[4\sqrt{6}]/15|=8/5`

`<=>[(x=[24+4\sqrt{6}]/15 (t//m)),(x=[-24+4\sqrt{6}]/15(ko t//m)):}`

Lời giải:

a.

$(5x-6)(1999^2+2.1999+1)=4.10^3$

$(5x-6)(1999+1)^2=(4.10^3)^2=4000^2$
$(5x-6).2000^2=4000^2$

$5x-6=\frac{4000^2}{2000^2}=2^2=4$

$5x=10$

$x=10:5=2$

b.

$(23545-7^5)x:[(8^4-4.10^3)^2-2478]=1$

$6738.x:6738=1$

$x=1$

\(5\sqrt{\dfrac{1}{2}}+\dfrac{1}{2}\sqrt{20}+\sqrt{5}\)

\(=\dfrac{5\sqrt{2}}{2}+\sqrt{5}+\sqrt{5}=\dfrac{5\sqrt{2}}{2}+2\sqrt{5}\)

\(=\dfrac{5\sqrt{2}}{2}+\dfrac{4\sqrt{5}}{2}=\dfrac{5\sqrt{2}+4\sqrt{5}}{2}\)

\(5\sqrt{\dfrac{1}{2}}+\dfrac{1}{2}\sqrt{20}+\sqrt{5}=\dfrac{5}{\sqrt{2}}+\dfrac{\sqrt{20}}{2}+\sqrt{5}=\dfrac{5\sqrt{2}+\sqrt{20}}{2}+\sqrt{5}=\dfrac{\sqrt{50}+\sqrt{20}}{\sqrt{4}}+\sqrt{5}=\dfrac{\sqrt{10}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{4}}+\sqrt{5}=\dfrac{\sqrt{5}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}+\sqrt{5}=\dfrac{5+\sqrt{10}+\sqrt{10}}{\sqrt{2}}=\dfrac{5+2\sqrt{10}}{\sqrt{2}}\)

Câu 19: 

\(=\dfrac{11x+x-18}{2x-3}=\dfrac{12x-18}{2x-3}=6\)

Câu 20: 

\(=\dfrac{3x+5}{x\left(x-5\right)}+\dfrac{x-25}{5\left(x-5\right)}\)

\(=\dfrac{15x+25+x^2-25x}{5x\left(x-5\right)}=\dfrac{\left(x-5\right)^2}{5x\left(x-5\right)}=\dfrac{x-5}{5x}\)

\(\dfrac{1}{2+\sqrt{3}}+\dfrac{1}{2-\sqrt{3}}\\ =\dfrac{2-\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}+\dfrac{2+\sqrt{3}}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}\\ =\dfrac{2-\sqrt{3}+2+\sqrt{3}}{2^2-\left(\sqrt{3}\right)^2}\\ =\dfrac{2+2}{4-3}\\ =4\)

Ta có: \(\dfrac{1}{2+\sqrt{3}}+\dfrac{1}{2-\sqrt{3}}\)

\(=2-\sqrt{3}+2+\sqrt{3}\)

=4

\(8,=\left(2x-3\right)\left(2x+3\right)\\ 9,=\left(1-5a^2\right)\left(1+5a^2\right)\)

8) \(-9+4x^2=\left(2x\right)^2-3^2=\left(2x-3\right)\left(2x+3\right)\)

9) \(1-25a^4=1-\left(5a^2\right)^2=\left(1-5a^2\right)\left(1+5a^2\right)\)

2) nH2=0,1(mol)

a) PTHH: Fe +2  HCl -> FeCl2 + H2

0,1______0,2______0,1____0,1(mol)

nFe=nH2=0,1(mol)

=>mFe=nFe.M(Fe)=0,1.56=5,6(g)

=> mFeO=mX-mFe= 9,2-5,6=3,6(g)

=> nFeO=mFeO/M(FeO)=3,6/72=0,05(mol)

PTHH: FeO +2 HCl -> FeCl2 + H2

0,05_________0,1___0,05__0,05(mol)

b) Sao lại mỗi oxit a, có một oxit thôi mà :(  Chắc % KL mỗi chất.

%mFeO=(mFeO/mhh).100%=(3,6/9,2).100=39,13%

=>%mFe=100%-%mFeO=100%-39,13%=60,87%

c) nHCl(tổng)= 2.nFe +2.nFeO=2.0,1+2.0,05=0,3(mol)

=>mHCl=nHCl.M(HCl)=0,3.36,5=10,95(g)

=>mddHCl=(mHCl.100%/C%ddHCl=(10,95.100)/7,3=150(g)

d) - Dung dich thu được chứa FeCl2.

mFeCl2=nFeCl2(tổng) . M(FeCl2)= (0,1+0,05).127=19,05(g)

mddFeCl2=mddHCl+mhh-mH2=150+9,2-0,1.2=159(g)

=> C%ddFeCl2=(mFeCl2/mddFeCl2).100%=(19,05/159).100=11,981%