Giải các phương trình sau:
9) x-49/ 50 + x-50/ 49 = 49/ x-50 + 50/ x-49
7) x+25/ 75 + x+30/70 = x+35/65 + x+40/60
8) 99-x/101 + 97-x/103 + 95-x/105 + 93-x/107 = 4
10) x+14/86 + x+15/85 + x+16/84 + x+17/83 + x+116/4 = 0
Giải các phương trình sau:
9) x-49/ 50 + x-50/ 49 = 49/ x-50 + 50/ x-49
7) x+25/ 75 + x+30/70 = x+35/65 + x+40/60
8) 99-x/101 + 97-x/103 + 95-x/105 + 93-x/107 = 4
10) x+14/86 + x+15/85 + x+16/84 + x+17/83 + x+116/4 = 0
7) \(\frac{x+25}{75}+\frac{x+30}{70}=\frac{x+35}{65}+\frac{x+40}{60}\)
\(\Leftrightarrow\)\(\frac{x+25}{75}+1+\frac{x+30}{70}+1=\frac{x+36}{65}+1+\frac{x+40}{60}+1\)
\(\Leftrightarrow\)\(\frac{x+100}{75}+\frac{x+100}{70}=\frac{x+100}{65}+\frac{x+100}{60}\)
\(\Leftrightarrow\)\(\left(x+100\right)\left(\frac{1}{75}+\frac{1}{70}-\frac{1}{65}-\frac{1}{60}\right)=0\)
\(\Leftrightarrow\)\(x+100=0\) (vì 1/75 + 1/70 - 1/65 - 1/60 \(\ne\)0)
\(\Leftrightarrow\)\(x=-100\)
Vậy.....
Giải các phương trình sau:
9) x-49/ 50 + x-50/ 49 = 49/ x-50 + 50/ x-49
7) x+25/ 75 + x+30/70 = x+35/65 + x+40/60
8) 99-x/101 + 97-x/103 + 95-x/105 + 93-x/107 = 4
10) x+14/86 + x+15/85 + x+16/84 + x+17/83 + x+116/4 = 0
7) \(\frac{x+25}{75}+\frac{x+30}{70}=\frac{x+35}{65}+\frac{x+40}{60}\)
\(\Leftrightarrow\)\(\frac{x+25}{75}+1+\frac{x+30}{70}+1=\frac{x+35}{65}+1+\frac{x+40}{60}+1\)
\(\Leftrightarrow\)\(\frac{x+100}{75}+\frac{x+100}{70}=\frac{x+100}{65}+\frac{x+100}{60}\)
\(\Leftrightarrow\)\(\left(x+100\right)\left(\frac{1}{75}+\frac{1}{70}-\frac{1}{65}-\frac{1}{60}\right)=0\)
\(\Leftrightarrow\)\(x+100=0\) (1/75 + 1/70 - 1/65 - 1/60 \(\ne\)0)
\(\Leftrightarrow\)\(x=-100\)
Vậy...
Giải các phương trình sau:
9) x-49/ 50 + x-50/ 49 = 49/ x-50 + 50/ x-49
8) 99-x/101 + 97-x/103 + 95-x/105 + 93-x/107 = 4
10) x+14/86 + x+15/85 + x+16/84 + x+17/83 + x+116/4 = 0
10) \(\frac{x+14}{86}+\frac{x+15}{85}+\frac{x+16}{84}+\frac{x+17}{83}+\frac{x+116}{4}=0\)
\(\Leftrightarrow\)\(\frac{x+14}{86}+1+\frac{x+15}{85}+1+\frac{x+16}{84}+1+\frac{x+17}{83}+1+\frac{x+116}{4}-4=0\)
\(\Leftrightarrow\)\(\frac{x+100}{86}+\frac{x+100}{85}+\frac{x+100}{84}+\frac{x+100}{83}+\frac{x+100}{4}=0\)
\(\Leftrightarrow\)\(\left(x+100\right)\left(\frac{1}{86}+\frac{1}{85}+\frac{1}{84}+\frac{1}{83}+\frac{1}{4}\right)=0\)
\(\Leftrightarrow\)\(x+100=0\) (vì 1/86 + 1/85 + 1/84 + 1/83 + 1/4 \(\ne\)0)
\(\Leftrightarrow\)\(x=-100\)
Vậy....
Giải phương trình:
h) \(\frac{99-x}{101}+\frac{97-x}{103}+\frac{95-x}{105}+\frac{93-x}{107}=-4\)
i) \(\frac{x+14}{86}+\frac{x+15}{85}+\frac{x+16}{84}+\frac{x+17}{83}+\frac{x+116}{4}=0\)
k) \(\left(\frac{8}{1.9}+\frac{8}{9.17}+...+\frac{8}{49.57}\right)+\frac{58}{57}+2\left(x-1\right)=\frac{2x+7}{3}+\frac{5x-8}{4}\)
l) \(\frac{5x-150}{50}+\frac{5x-102}{49}+\frac{5x-56}{48}+\frac{5x-12}{47}+\frac{5x-660}{46}=0\)
các bạn không giải thì làm ơn đừng trả lời
\(h.\) \(\frac{99-x}{101}+\frac{97-x}{103}+\frac{95-x}{105}+\frac{93-x}{107}=-4\)
\(\Leftrightarrow\) \(\frac{99-x}{101}+\frac{97-x}{103}+\frac{95-x}{105}+\frac{93-x}{107}+4=0\)
\(\Leftrightarrow\) \(\left(\frac{99-x}{101}+1\right)+\left(\frac{97-x}{103}+1\right)+\left(\frac{95-x}{105}+1\right)+\left(\frac{93-x}{107}\right)=0\)
\(\Leftrightarrow\) \(\frac{200-x}{101}+\frac{200-x}{103}+\frac{200-x}{105}+\frac{200-x}{107}=0\)
\(\Leftrightarrow\) \(\left(200-x\right)\left(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\right)=0\)
\(\Leftrightarrow\) \(200-x=0\) \(\Leftrightarrow\) \(x=200\)
a,\(\frac{x+14}{86}+\frac{x+15}{85}+\frac{x+16}{84}+\frac{x+17}{83}+\frac{x+116}{4}=0\)\(=0\)
b,\(\frac{x-49}{50}+\frac{x-50}{49}=\frac{49}{50-x}+\frac{50}{49-x}\)
(-làm đc 1 câu=1 tick
-làm đc 2 câu=2 tick)
a) \(\frac{x+14}{86}+\frac{x+15}{85}+\frac{x+16}{84}+\frac{x+17}{83}+\frac{x+116}{4}=0\)
\(\Leftrightarrow\)\(\frac{x+14}{86}+1+\frac{x+15}{85}+1+\frac{x+16}{84}+1+\frac{x+17}{83}+1+\frac{x+116}{4}-4=0\)
\(\Leftrightarrow\)\(\frac{x+100}{86}+\frac{x+100}{85}+\frac{x+100}{84}+\frac{x+100}{83}+\frac{x+100}{4}=0\)
\(\Leftrightarrow\)\(\left(x+100\right)\left(\frac{1}{86}+\frac{1}{85}+\frac{1}{84}+\frac{1}{83}+\frac{1}{4}\right)=0\)
\(\Leftrightarrow\)\(x+100=0\)
\(\Leftrightarrow\)\(x=-100\)
Vậy...
câu 1:=\(\frac{x+14}{86}+1+\frac{x+15}{85}+1+\frac{x+16}{84}+1+\frac{x+17}{83}+1+\frac{x+116}{4}-4=0\)
=\(\frac{x+100}{86}+\frac{x+100}{85}+\frac{x+100}{84}+\frac{x+100}{83}+\frac{x+100}{4}=0\)
=\(^{(x+100).(\frac{1}{86}+\frac{1}{85}+\frac{1}{84}+\frac{1}{83}+\frac{1}{4})=0}\)
=\(\orbr{\begin{cases}100+x=0\\\frac{1}{86}+\frac{1}{85}+\frac{1}{84}+\frac{1}{83}+\frac{1}{4}=0\left(voly\right)\end{cases}}\Leftrightarrow100+x=0\Leftrightarrow x=-100\)
Giải phương trình:
a)\(\dfrac{x-49}{50}\)+\(\dfrac{x-50}{49}=\dfrac{49}{x-50}+\dfrac{50}{x-49}\)
b)\(\dfrac{x+14}{86}+\dfrac{x+15}{85}+\dfrac{x+16}{84}+\dfrac{x+17}{83}+\dfrac{x+116}{4}=0\)
c)\(\dfrac{1}{\left(x^2+5\right)\left(x^2+4\right)}+\dfrac{1}{\left(x^2+4\right)\left(x^2+3\right)}+\dfrac{1}{\left(x^2+3\right)\left(x^2+2\right)}+\dfrac{1}{\left(x^2+2\right)\left(x^2+1\right)}=-1\)
b)\(\dfrac{x+14}{86}+\dfrac{x+15}{85}+\dfrac{x+16}{84}+\dfrac{x+17}{83}+\dfrac{x+116}{4}=0\)
\(\Leftrightarrow\dfrac{x+14}{86}+1+\dfrac{x+15}{85}+1+\dfrac{x+16}{84}+1+\dfrac{x+17}{83}+1+\dfrac{x+116}{4}-4=0\)
\(\Leftrightarrow\dfrac{x+100}{86}+\dfrac{x+100}{85}+\dfrac{x+100}{84}+\dfrac{x+100}{83}+\dfrac{x+100}{4}=0\)
\(\Leftrightarrow\left(x+100\right)\left(\dfrac{1}{86}+\dfrac{1}{85}+\dfrac{1}{84}+\dfrac{1}{83}+\dfrac{1}{4}\right)=0\)
\(\Leftrightarrow x+100=0\).Do \(\dfrac{1}{86}+\dfrac{1}{85}+\dfrac{1}{84}+\dfrac{1}{83}+\dfrac{1}{4}\ne0\)
\(\Leftrightarrow x=-100\)
c)\(\dfrac{1}{\left(x^2+5\right)\left(x^2+4\right)}+\dfrac{1}{\left(x^2+4\right)\left(x^2+3\right)}+\dfrac{1}{\left(x^2+3\right)\left(x^2+2\right)}+\dfrac{1}{\left(x^2+2\right)\left(x^2+1\right)}=-1\)
\(\Leftrightarrow\dfrac{1}{\left(x^2+1\right)\left(x^2+2\right)}+\dfrac{1}{\left(x^2+2\right)\left(x^2+3\right)}+...+\dfrac{1}{\left(x^2+4\right)\left(x^2+5\right)}=-1\)
\(\Leftrightarrow\dfrac{1}{x^2+1}-\dfrac{1}{x^2+2}+\dfrac{1}{x^2+2}-\dfrac{1}{x^2+3}+...+\dfrac{1}{x^2+4}-\dfrac{1}{x^2+5}=-1\)
\(\Leftrightarrow\dfrac{1}{x^2+1}-\dfrac{1}{x^2+5}=-1\)\(\Leftrightarrow\dfrac{4}{x^4+6x^2+5}=-1\)
\(\Leftrightarrow\dfrac{x^4+6x^2+9}{x^4+6x^2+5}=0\Leftrightarrow x^4+6x^2+9=0\)
\(\Leftrightarrow\left(x^2+3\right)^2>0\forall x\) (vô nghiệm)
Giải Phương trình
1)\(\dfrac{99-x}{101}+\dfrac{97-x}{103}+\dfrac{95-x}{105}+\dfrac{93-x}{107}=4\)
2)\(\dfrac{x+14}{86}+\dfrac{x+15}{85}+\dfrac{x+16}{84}+\dfrac{x+17}{83}+\dfrac{x+116}{4}=0\)
3)\(x+\dfrac{2x+\dfrac{x-1}{5}}{3}=1-\dfrac{3x-\dfrac{1-2x}{3}}{5}\)
Bài 1:
\(\frac{99-x}{101}+\frac{97-x}{103}+\frac{95-x}{105}+\frac{93-x}{107}=-4\)
\(\Leftrightarrow \frac{99-x}{101}+1+\frac{97-x}{103}+1+\frac{95-x}{105}+1+\frac{93-x}{107}+1=0\)
\(\Leftrightarrow \frac{99-x+101}{101}+\frac{97-x+103}{103}+\frac{95-x+105}{105}+\frac{93-x+107}{107}=0\)
\(\Leftrightarrow \frac{200-x}{101}+\frac{200-x}{103}+\frac{200-x}{105}+\frac{200-x}{107}=0\)
\(\Leftrightarrow (200-x)\left(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\right)=0\)
Vì \(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\neq 0\) nên suy ra \(200-x=0\Rightarrow x=200\)
Bài 2:
\(\frac{x+14}{86}+\frac{x+15}{85}+\frac{x+16}{84}+\frac{x+116}{4}=0\)
\(\Leftrightarrow \frac{x+14}{86}+1+\frac{x+15}{85}+1+\frac{x+16}{84}+1+\frac{x+17}{83}+1+\frac{x+116}{4}-4=0\)
\(\Leftrightarrow \frac{x+100}{86}+\frac{x+100}{85}+\frac{x+100}{84}+\frac{x+100}{83}+\frac{x+100}{4}=0\)
\(\Leftrightarrow (x+100)\left(\frac{1}{86}+\frac{1}{85}+\frac{1}{84}+\frac{1}{83}+\frac{1}{4}\right)=0\)
Vì \(\frac{1}{86}+\frac{1}{85}+\frac{1}{84}+\frac{1}{83}+\frac{1}{4}\neq 0\). Do đó \(x+100=0\Rightarrow x=-100\)
1/
99-x/101+97-x/103+95-x/105+93-x/107
\(\Leftrightarrow\)(99-x/101+1)+(97-x/103+1)+(95-x/105+1)+(93-x/107+1)=0
\(\Leftrightarrow\)100-x/101+100-x/103+100-x/105+100-x/107=0
\(\Leftrightarrow\)(100-x)(1/101+1/103+1/105+1/107)=0
\(\Leftrightarrow\)100-x=0\(\Leftrightarrow\)
x=-100
Giải phương trình sau \(\frac{50}{x-49}+\frac{49}{x-50}=\frac{x-49}{50}+\frac{x-50}{49}\):
\(ĐKXĐ:x\ne49;x\ne50\)
Đặt \(x-49=u;x-50=v\)
Phương trình trở thành \(\frac{50}{u}+\frac{49}{v}=\frac{u}{50}+\frac{v}{49}\)
\(\Rightarrow\frac{50v+49u}{uv}=\frac{49u+50v}{2450}\)
\(\Rightarrow\orbr{\begin{cases}50v+49u=0\\uv=2450\end{cases}}\)
+) \(50v+49u=0\)
\(\Rightarrow50v=-49u\)
\(\Rightarrow\frac{v}{-49}=\frac{u}{50}=\frac{\left(x-50\right)-\left(x-49\right)}{-49-50}\)
\(=\frac{-1}{-99}=\frac{1}{99}\)
\(\Rightarrow\hept{\begin{cases}v=\frac{-49}{99}\\u=\frac{50}{99}\end{cases}}\Rightarrow x=\frac{4901}{99}\)(tm)
+) \(uv=2450\)
hay \(\left(x-49\right)\left(x-50\right)=2450\)
\(\Leftrightarrow x^2-99x+2450=2450\)
\(\Leftrightarrow x^2-99x=0\Leftrightarrow x\left(x-99\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=99\end{cases}}\left(tm\right)\)
Vậy phương trình có 3 nghiệm \(S=\left\{0;\frac{4901}{99};99\right\}\)
bài 1 : 101 x 125 + 101 x 25 - 101 x 50
bài 2 : 76 x 115 + 56 x 24 + 59 x 24
bài 3 : thực hiện phép tính : a ) 90-84+ 8 - 72 +66-60+54-48
b ) 99-97+95-93+91-89+.........+7-5+3-1
bài 4 : tìm số tự nhiên x biết :
a) \(x\) x 16 -\(x\) x 9 = 56
bài 5 :tìm số tự nhiên x , biết
a) \(x\) + 2 x \(x\) +3 x \(x\)+4 x \(x\) +5 x \(x\) = 165
b ) 1+2+3+4+.....+\(x\)=55
GIẢI GIÚP E Ạ
Bài 1:
\(101\cdot125+101\cdot25-101\cdot50\)
\(=101\cdot\left(125+25-50\right)\)
\(=101\cdot100\)
\(=10100\)
Bài 2:
\(76\cdot115+56\cdot24+59\cdot24\)
\(=76\cdot115+24\cdot\left(56+59\right)\)
\(=76\cdot115+24\cdot115\)
\(=115\cdot\left(76+24\right)\)
\(=115\cdot100\)
\(=11500\)
5:
a: =>15x=165
=>x=11
b: =>x(x+1)/2=55
=>x^2+x=110
=>x=10
4: =>7x=56
=>x=8
Bài 1:
101•125+101•25+101•50
= 101•(125+25-50)
=101•100
=10100
Bài 2:
76•115+56•24+59•24
= 76•115+24•(56+59)
= 76•115+24•115
= 115•(76+24)
= 115•100
= 11500