(3x+13).23_24=22.3.23
\(Giảiphươngtrình:\sqrt{7+3x}+\sqrt{13-3x}+5\cdot\sqrt{\left(7+3x\right)\left(13-3x\right)}=46\)
\(\left(\sqrt{7+3x}-4\right)+\left(\sqrt{13-3x}-2\right)+5.\left(\sqrt{\left(7+3x\right)\left(13-3x\right)}-8\right)=0\)
=) \(\frac{7+3x-16}{\sqrt{7+3x}+4}+\frac{13-3x-4}{\sqrt{13-3x}+2}+5.\left(\sqrt{91+18x-9x^2}-8\right)=0\)
=) \(\frac{3\left(x-3\right)}{\sqrt{7+3x}+4}+\frac{3\left(3-x\right)}{\sqrt{13-3x}+2}+\frac{5\left(27+18x-9x^2\right)}{\sqrt{91+18x-9x^2}+8}=0\)
=) \(\frac{3\left(x-3\right)}{\sqrt{7+3x}+4}-\frac{3\left(x-3\right)}{\sqrt{13-3x}+2}-\frac{45\left(x+1\right)\left(x-3\right)}{\sqrt{91+18x-9x^2}+8}=0\)
=) đến đây chắc là tự làm đc rồi
giải pt : \(\sqrt{7+3x}+\sqrt{13-3x}+5\sqrt{\left(7+3x\right)\left(13-3x\right)}=46\)
Đặt \(\sqrt{7+3x}=a;\sqrt{13-3x}=b\)
=>a+b+5ab=46
=>(a+b)^2=46-5ab
=>a^2+b^2+2ab=2116-460ab+25a^2b^2
=>25a^2b^2-460ab+2116=7+3x+13-3x+2ab
=>25a^2b^2-462ab+2096=0
=>\(\left[{}\begin{matrix}ab=\dfrac{262}{25}\\ab=8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\left(7+3x\right)\cdot\left(13-3x\right)=109.8304\\\left(7+3x\right)\left(13-3x\right)=64\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}91-21x+39x-9x^2=109.8304\\91-21x+39x-9x^2=64\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-9x^2+18x-18.8304=0\\-9x^2+18x+27=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
Giải phương trình : \(\sqrt{7+3x}+\sqrt{13-3x}+5\sqrt{\left(7+3x\right)\left(13-3x\right)}=46\)
a)5-(13-3x)=109-(32+109)
b)/3x-6/+(x-2^2)=0
c)/7-2x/=-13-5.(-8)
a)5-(13-3x)=109-(32+109)
5-(13-3x)=-32
13-3x =37
3x =-24
3x =-6
a)5-(13-3x)=109-(32+109)
5-13+3x =109-32-109
-8+3x=-32
3x=-32-(-8)
3x=-24
x=-24:3
x=-8
b)|3x-6|+(x-22)=0
(3x-6)+(x-22)=0
3x-6+x-22=0
3x+x=0+6+22
4x=10
x=\(\dfrac{5}{2}\)
c)/7-2x/=-13-5.(-8)
|7-2x|=27
⇒7-2x=27 hoặc 7-2x=-27
x=-10 hoặc x=-17
Tìm x y biết
a)xy+3x-2y=11
b)2x^2-2xy+x-y=12
c)2xy-10y-x=13
e)xy-2y^2+8y-3x=13
f)xy-2y^2+8y-3x=13
\(a)xy+3x-2y=11\)
\(\Leftrightarrow xy+3x-2y-6=5\)
\(\Leftrightarrow x\left(y+3\right)-2\left(y+3\right)=5\)
\(\Leftrightarrow\left(y+3\right)\left(x-2\right)=5\)
\(\Leftrightarrow\hept{\begin{cases}y+3=-1\\x-2=-5\end{cases}}\Leftrightarrow\hept{\begin{cases}y=-4\\x=-3\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}y+3=1\\x-2=5\end{cases}}\Leftrightarrow\hept{\begin{cases}y=-2\\x=7\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}y+3=-5\\x-2=-1\end{cases}}\Leftrightarrow\hept{\begin{cases}y=-8\\x=1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}y+3=5\\x-2=1\end{cases}}\Leftrightarrow\hept{\begin{cases}y=2\\x=3\end{cases}}\)
\(b)2x^2-2xy+x-y=12\)
\(\Leftrightarrow2x\left(x-y\right)+\left(x-y\right)=12\)
\(\Leftrightarrow\left(x-y\right)\left(2x+1\right)=12\)
\(\Rightarrow\left(x-y\right);\left(2x+1\right)\inƯ\left(12\right)\)
\(\RightarrowƯ\left(12\right)\in\left\{-1;1;-2;2;-3;3;-4;4;-6;6;-12;12\right\}\)
Vì 2x+1 luôn lẻ
\(\Rightarrow2x+1\in\left\{-1;1;-3;3\right\}\)
\(\Leftrightarrow\hept{\begin{cases}2x+1=-1\\x-y=-12\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-1\\y=11\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}2x+1=1\\x-y=12\end{cases}}\Leftrightarrow\hept{\begin{cases}x=0\\y=-12\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}2x+1=-3\\x-y=-4\end{cases}}\Leftrightarrow\hept{\begin{cases}x=-2\\y=2\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}2x+1=3\\x-y=4\end{cases}}\Leftrightarrow\hept{\begin{cases}x=1\\y=-3\end{cases}}\)
\(c)2xy-10y-x=13\)
\(\Leftrightarrow x\left(2y-1\right)-2y.5+5=18\)
\(\Leftrightarrow x\left(2y-1\right)-5\left(2y-1\right)=18\)
\(\Leftrightarrow\left(2y-1\right)\left(x-5\right)=18\)
\(\Leftrightarrow2y-1;x-5\inƯ\left(18\right)\)
\(\RightarrowƯ\left(18\right)\in\left\{-1;1;-2;2;-3;3;-6;6;-9;9;-18;18\right\}\)
Vì 2y-1 luôn lẻ
=>2y-1 thuộc {-1;1;-3;3;-9;9}
=> Làm tương tự nhé
\(e)xy-2y^2+8y-3x=13\)
\(\Leftrightarrow xy-2y^2+2y+6y-3x-6=7\)
\(\Leftrightarrow y\left(x-2y+2\right)+3\left(-x+2y-2\right)=7\)
\(\Leftrightarrow y\left(x-2y+2\right)-3\left(x-2y+2\right)=7\)
\(\Leftrightarrow\left(x-2y+2\right)\left(y-3\right)=7\)
Tự khai triển như các câu trên.
Mình đg bận nên ko lm đc hết câu.
( 5^3.(3x+2) :13= 5^5:(13^5 :13^4)
\(\left[5^3.\left(3x+2\right)\right]:13=5^5:\left(13^5:13^4\right)\)
\(\left[5^3\left(3x+2\right)\right]:13=5^5:13\)
\(\left[5^3\left(3x+2\right)\right]:13=\frac{3125}{13}\)
\(\left[5^3\left(3x+2\right)\right]=3125\)
\(3x+2=3125:5^3\)
\(3x+2=25\)
\(3x=25-2\)
\(3x=23\)
\(x=\frac{23}{3}\)
\(5^3.\left(3x+2\right):13=5^5:\left(13^5:13^4\right)\)
\(5^3.\left(3x+2\right):13=3125:13\)
\(5^3.\left(3x+2\right):13=\frac{3125}{13}\)
125 . ( 3x + 2 ) : 13 =\(\frac{3125}{13}\)
125 . ( 3x + 2 ) =\(\frac{3125}{13}.\frac{13}{1}=3125\)
3x + 2 = 3125 : 125
3x + 2 = 25
3x = 25 -2
3x = 23
x = 23 : 3
x = \(\frac{23}{3}\)
bài này tui làm cho cậu cậu tick rồi mà
5^3(3x+2):13=10^3:(13^5:13^4)
\(5^3\left(3x+2\right)\div13=10^3\div\left(13^5\div13^4\right)\)
\(\Rightarrow125\left(3x+2\right)\div13=1000\div13\)
\(\Rightarrow125\left(3x+2\right)=1000\)
\(\Rightarrow3x+2=1000\div125\)
\(\Rightarrow3x+2=8\)
\(\Rightarrow3x=8-2\)
\(\Rightarrow3x=6\Rightarrow x=6\div3\Rightarrow x=2\)
Vậy : x = 2
( 5^3 . (3x + 2) ) : 13=5^5 : ( 13^5 : 13^4)
\(\left[5^3\left(3x+2\right)\right]:13=5^5:\left(13^5:13^4\right)\)
\(\left[5^3\left(3x+2\right)\right]:13=5^5:13\)
\(5^3\left(3x+2\right)=5^5:13.13\)
\(5^3\left(3x+2\right)=5^5\)
\(3x+2=5^5:5^3\)
\(3x+2=25\)
\(3x=25-2\)
\(3x=23\)
\(\Rightarrow x=\frac{23}{3}\)
( 375x+250 ) :13=3125;13
375x+250=3125
375x=2875
x=23/3
tim x biet 2/3x-(70+10/11):(13/15+13/35+13/63+13/99)=-5
x = 60 nha bn !!!
có cần cách giải ko , mik ghi cho
A) 7/3x+5 = 9/6x-7
B) 3x+6/4 = 5-7x/6
C) 12/5x+6 = 17/3x+12
D) 6(3x+7) = 12(2x-4)
E) 13(2x-9)= 8(3x-13)
Giải rõ giùm em với
\(a,\frac{7}{3}x+5=\frac{9}{6}x-7\)
\(\frac{7}{3}x-\frac{9}{6}x=-7-5\)
\(\left(\frac{7}{3}-\frac{9}{6}\right).x=-12\)
\(\frac{5}{6}.x=-12\)
\(x=\left(-12\right):\frac{5}{6}\)
\(x=-\frac{72}{5}\)
\(b,3x+\frac{6}{4}=5-\frac{7x}{6}\)
\(3x+\frac{7x}{6}=5-\frac{6}{4}\)
\(\left(3+\frac{7}{6}\right).x=\frac{7}{2}\)
\(\frac{25}{6}.x=\frac{7}{2}\)
\(x=\frac{7}{2}:\frac{25}{6}\)
\(x=\frac{21}{25}\)
\(c,\frac{12}{5}x+6=\frac{17}{3}x+12\)
\(\frac{12}{5}x-\frac{17}{3}x=12-6\)
\(-\frac{49}{15}x=6\)
\(x=6:\left(-\frac{49}{15}\right)\)
\(x=-\frac{90}{49}\)
\(d,6\left(3x+7\right)=12\left(2x-4\right)\)
\(18x+42=24x-48\)
\(18x-24x=-48-42\)
\(-6x=-90\)
\(x=15\)
\(e,13\left(2x-9\right)=8\left(3x-13\right)\)
\(26x-117=24x-104\)
\(26x-24x=-104+117\)
\(2x=13\)
\(x=\frac{13}{2}\)