HOC24
Lớp học
Môn học
Chủ đề / Chương
Bài học
`a)(x-2)/3=5/4`
`=>4(x-2)=3*5`
`=>4(x-2)=15`
`=>x-2=15/4`
`=>x=15/4+2`
`=>x=23/4`
`b)|3x-1|-3=8`
`=>|3x-1|=8+3=11`
TH1: `3x-1=11`
`=>3x=11+1=12`
`=>x=12:3=4`
TH2: `3x-1=-11`
`=>3x=-11+1=-10`
`=>x=-10/3`
`c)(x-1)^2=(x-1)^4`
`=>(x-1)^4-(x-1)^2=0`
`=>(x-1)^2[(x-1)^2-1]=0`
`=>(x-1)^2(x-1-1)(x-1+1)=0`
`=>(x-1)^2x(x-2)=0`
TH1: `(x-1)^2=0`
`=>x=1`
TH2: `x=0`
TH3: `x-2=0`
`=>=x=2`
`(x-2)^3-x(x-2)(x+2)+6x(x-3)`
`=(x^2-3*x^2*2+3*x*2^2-2^3)-x(x^2-4)+6x^2-18x`
`=x^3-6x^2+12x-8-x^3+4x+6x^2-18x`
`=(x^3-x^3)+(6x^2-6x^2)+(12x-18x)-8`
`=-6x-8`
`2^(x+3)+2^x=144`
`=>2^x*2^3+2^x=144`
`=>2^x*(2^3+1)=144`
`=>2^x*9=144`
`=>2^x=144:9`
`=>2^x=16`
`=>2^x=2^4`
`=>x=4`
`3^x+3^(x+2)=2430`
`=>3^x+3^x*3^2=2430`
`=>3^x*(1+3^2)=2430`
`=>3^x*10=2430`
`=>3^x=2430:10`
`=>3^x=243`
`=>3^x=3^5`
`=>x=5`
`5^6:5^4+3*3^2-2021^0`
`=5^(6-4)+3^(1+2)-1`
`=5^2+3^3-1`
`=25+27-1`
`=52-1`
`=51`
`a)(-5/9)^10:x=(-5/9)^8`
`<=>x=(-5/9)^10:(-5/9)^8`
`<=>x=(-5/9)^2`
`<=>x=25/81`
`b)|x|-3/5=5/9`
`<=>|x|=5/9+3/5`
`<=>|x|=52/45`
`<=>x=+-52/45`
`c)|x+3/4|=1/2`
`TH1:x+3/4=1/2`
`<=>x=1/2-3/4`
`<=>x=-1/4`
`TH2:x+3/4=-1/2`
`<=>x=-1/2-3/4`
`<=>x=-5/4`
`d)|x-3/4|+|2/5-y|+|3+z|=0`
Ta có:
`|x-3/4|>=0` với mọi x
`|2/5-y|>=0` với mọi y
`|3+z|>=0` với mọi z
`=>|x-3/4|+|2/5-y|+|3+z|>=0` với mọi x,y,z
Dấu "=" xảy ra: `x-3/4=0` và `2/5-y=0` và `3+z=0`
`<=>x=3/4` và `y=2/5` và `z=-3`
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`
`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`
`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`
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`
`3)5^x=5^3*5^5`
`=>5^x=5^8`
`4)8^x=8^3*8^5`
`=>8^x=8^8`
`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`