Câu 2:

`a)20-(x+14)=5`

`<=>20-x-14=5`

`<=>6-x=5`

`<=>x=6-5`

`<=>x=1`

`b)24+3(5-x)=27`

`<=>3(5-x)=27-24`

`<=>3(5-x)=3`

`<=>5-x=3/3=1`

`<=>x=5-1`

`<=>x=4`

`c)2^(x+3)+2^x=144`

`<=>2^x*(2^3+1)=144`

`<=>2^x*9=144`

`<=>2^x=144:9`

`<=>2^x=4^2`

`<=>2^x=(2^2)^2=2^4`

`<=>x=4`

`d)3^x+3^(x+2)=2430`

`<=>3^x*(1+3^2)=2430`

`<=>3^x=2430:10`

`<=>3^x=243`

`<=>3^x=3^5`

`<=>x=5` 

`a)(x-1)^2=6`

\(\Leftrightarrow\left[{}\begin{matrix}x-1=\sqrt{6}\\x-1=-\sqrt{6}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=1+\sqrt{6}\\x=1-\sqrt{6}\end{matrix}\right.\)

`b)3x^2-6=0`

`<=>3x^2=6`

`<=>x^2=2`

\(\Leftrightarrow x=\pm\sqrt{2}\)

`c)(x-2)(2x+1)=0`

`TH1:x-2=0`

`<=>x=2`

`TH2:2x+1=0`

`<=>2x=-1`

`<=>x=-1/2`

`d)x^2-4x+4=0`

`<=>(x-2)^2=0`

`<=>x=2`

`e)x^2-8x+7=0`

`<=>(x^2-x)+(-7x+7)=0`

`<=>x(x-1)-7(x-1)=0`

`<=>(x-1)(x-7)=0`

TH1: `x-1=0`

`<=>x=1`

TH2: `x-7=0`

`<=>x=7`

`f)x^4-256=0`

`<=>(x^2-16)(x^2+16)=0`

`<=>(x-4)(x+4)(x^2+16)=0`

Mà: `x^2+16>=16>0`

`=>x-4=0` hoặc `x+4=0`

`<=>x=+-4` 

`1/2-x-1/3=5/6`

`=>1/6-x=5/6`

`=>x=1/6-5/6`

`=>x=-4/6=-2/3`

`5/12-(3/8-x)=-5/6`

`=>5/12-3/8+x=-5/6`

`=>1/24+x=-5/6`

`=>x=-5/6-1/24`

`=>x=-21/24=-7/8`

`3/4-(x-2/3)=5/6`

`=>3/4-x+2/3=5/6`

`=>17/12-x=5/6`

`=>x=17/12-5/6`

`=>x=7/12`

`-7/12-3/5-x=3/4`

`=>-71/60-x=3/4`

`=>x=-71/60-3/4`

`=>x=-116/60=-29/15` 

`7/2-(3/8-x)=-5/6`

`=>7/2-3/8+x=-5/6`

`=>25/8+x=-5/6`

`=>x=-5/6-25/8`

`=>x=-95/24` 

`(x+98)/2+(x+45)/55+(x-1)/101=(x+5)/95+(x+30)/70+(x-3)/103`

`=>((x+98)/2+1)+((x+45)/55+1)+((x-1)/101+1)=((x+5)/95+1)+((x+30)/70+1)+((x-3)/103+1)`

`=>(x+100)/2+(x+100)/55+(x+100)/101=(x+100)/95+(x+100)/70+(x+100)/103`

`=>(x+100)/2+(x+100)/55+(x+100)/101-(x+100)/95-(x+100)/70-(x+100)/103=0`

`=>(x+100)(1/2+1/55+1/10-1/96-1/70-1/103)=0`

`=>x+100=0`

`=>x=-100` 

Bài 2:

`1)4^x=4^3*4^5`

`=>4^x=4^8`

`=>x=8`

`2)7^x=7*7^7`

`=>7^x=7^8`

`=>x=8`

`3)5^x=5^3*5^5`

`=>5^x=5^8`

`=>x=8`

`4)8^x=8^3*8^5`

`=>8^x=8^8`

`=>x=8`

`5)5^x=5^15:5^3`

`=>5^x=5^12`

`=>x=12`

`6)9^x=9^20:9^5`

`=>9^x=9^15`

`=>x=15`

`7)4^x=4^15:4^5`

`=>4^x=4^10`

`=>x=10`

`8)7^x=7^20:7^10`

`=>7^x=7^10`

`=>x=10` 

`f)1-2m+m^2-x^2-4x-4`

`=(m^2-2m+1)-(x^2+4x+4)`

`=(m-1)^2-(x+2)^2`

`=(m-1-x-2)(m-1+x+2)`

`=(m-x-3)(m+x+1)`

`g)100a^2-(a^2+25)^2`

`=(10a)^2-(a^2+25)^2`

`=(-a^2+10a-25)(a^2+10a+25)`

`=-(a^2-10a+25)(a+5)^2`

`=-(a-5)^2+(a-5)^2`

`h)10x^2-7x-3`

`=(10x^2-10x)+(3x-3)`

`=10x(x-1)+3(x-1)`

`=(x-1)(10x+3)`

`j)(x^2+x)^2+4x^2+4x-12`

`=(x^2+x)^2+4(x^2+x)-12`

`=[(x^2+x)^2-2(x^2+x)]+[6(x^2+x)-12]`

`=(x^2+x)(x^2+x-2)+6(x^2+x-2)`

`=(x^2+x-2)(x^2+x+6)`

`=(x-1)(x+2)(x^2+x+6)`

`k)(x^2+x+1)(x^2+x+2)-12`

`=(x^2+x)^2+3(x^2+x)+2-12`

`=(x^2+x)^2+3(x^2+x)-10`

`=[(x^2+x)^2-2(x^2+x)]+[5(x^2+x)-10]`

`=(x^2+x)(x^2+x-2)+5(x^2+x-2)`

`=(x^2+x-2)(x^2+x+5)`

`=(x-1)(x+2)(x^2+x+5)` 

`a)20x^3y^4-5x^2y^3+100x^2y^4`

`=5x^2y^3(4xy-1+20y)`

`b)x^2-xy-15x+15y`

`=x(x-y)-15(x-y)`

`=(x-15)(x-y)`

`c)2x^3+8x^2+8x`

`=2x(x^2-4x+4)`

`=2x(x-2)^2`

`d)x^3-27y^6`

`=x^3-(3y^2)^3`

`=(x-3y)(x^2+3xy^2+9y^4)` 

`e)36x^2-a^2+10a-25`

`=36x^2-(a^2-10a+25)`

`=(6x)^2-(a-5)^2`

`=(6x-a+5)(6x+a-5)` 

`1)-3/5+7/10`

`=-6/10+7/10`

`=1/10`

`2)-7/12-8/15`

`=-35/60-32/60`

`=-67/60`

`3)0,75+1/8`

`=3/4+1/8`

`=6/8+1/8`

`=7/8`

`4)-3 1/8-(-0,12)`

`=-3-1/8+3/25`

`=-25/8+3/25`

`=-601/200`

`5)1,25+(-5/8)+(-5/2)`

`=5/4-5/8-5/2`

`=10/8-5/8-20/8`

`=-15/8`

`(2^43+2^4):(2^39+1)`

`=(2^4*2^39+2^4*1):(2^39+1)`

`=2^4*(2^39+1):(2^39+1)`

`=2^4`

`=16` 

Ta có: 

`(x+4)/(x-2)+(2x+5)/(x-2)` (x khác 2)

`=(x+4+2x+5)/(x-2)`

`=(3x+9)/(x-2)`

`=(3x-6+15)/(x-2)`

`=(3(x-2)+15)/(x-2)`

`=3+15/(x-2)`

Để giá trị của bt nguyên thì:

x - 2 ∈ Ư(15) = {1; -1; 3; -3; 5; -5; 15; -15}

=> x ∈ {3; 1; 5; -1; 7; -3; 17; -13}