Giải từng bước giúp em với ạ
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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.
$(23545-7^5)x:[(8^4-4.10^3)^2-2478]=1$
$6738.x:6738=1$
$x=1$
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%
`(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)):}`
\(=\left(5x^2+10xy\right)-\left(4x+8y\right)\)
\(=5x\left(x+2y\right)-4\left(x+2y\right)\)
\(=\left(x+2y\right)\left(5x-4\right)\)
\(5\sqrt{\dfrac{1}{2}}+\dfrac{1}{2}\sqrt{20}+\sqrt{5}\)
\(=\dfrac{5\sqrt{2}}{2}+\sqrt{5}+\sqrt{5}=\dfrac{5\sqrt{2}}{2}+2\sqrt{5}\)
\(=\dfrac{5\sqrt{2}}{2}+\dfrac{4\sqrt{5}}{2}=\dfrac{5\sqrt{2}+4\sqrt{5}}{2}\)
\(5\sqrt{\dfrac{1}{2}}+\dfrac{1}{2}\sqrt{20}+\sqrt{5}=\dfrac{5}{\sqrt{2}}+\dfrac{\sqrt{20}}{2}+\sqrt{5}=\dfrac{5\sqrt{2}+\sqrt{20}}{2}+\sqrt{5}=\dfrac{\sqrt{50}+\sqrt{20}}{\sqrt{4}}+\sqrt{5}=\dfrac{\sqrt{10}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{4}}+\sqrt{5}=\dfrac{\sqrt{5}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}+\sqrt{5}=\dfrac{5+\sqrt{10}+\sqrt{10}}{\sqrt{2}}=\dfrac{5+2\sqrt{10}}{\sqrt{2}}\)