Giải các phương trình sau:
a) \({5^{2x - 1}} = 25\);
b) \({3^{x + 1}} = {9^{2x + 1}}\);
c) \({10^{1 - 2x}} = 100000\).
Bài 1. Giải các phương trình sau:
a) |4x2 - 25| = 0
b) |x - 2| = 3
c) |x - 3| = 2x - 1
d) |x - 5| = |3x - 2|
Lời giải:
a) $|4x^2-25|=0$
$\Leftrightarrow 4x^2-25=0$
$\Leftrightarrow (2x-5)(2x+5)=0$
$\Rightarrow x=\pm \frac{5}{2}$
b)
$|x-2|=3$
\(\Rightarrow \left[\begin{matrix} x-2=-3\\ x-2=3\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=-1\\ x=5\end{matrix}\right.\)
c)
\(|x-3|=2x-1\Rightarrow \left\{\begin{matrix} 2x-1\geq 0\\ \left[\begin{matrix} x-3=2x-1\\ x-3=1-2x\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow \left\{\begin{matrix} x\geq \frac{1}{2}\\ \left[\begin{matrix} x=-2\\ x=\frac{4}{3}\end{matrix}\right.\end{matrix}\right.\Rightarrow x=\frac{4}{3}\)
d)
$|x-5|=|3x-2|$
\(\Rightarrow \left[\begin{matrix} x-5=3x-2\\ x-5=2-3x\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} x=\frac{-3}{2}\\ x=\frac{7}{4}\end{matrix}\right.\)
Câu 1: Giải các phương trình sau:
a) 3- 4x (25 - 2x ) = 8x2 + x - 300
b)
c)
Giải các phương trình sau:
a/ 3x – 2 = 2x – 3
b/ 7 – 2x = 22 – 3x
c) 8x – 3 = 5x + 12
d/ x – 12 + 4x = 25 + 2x – 1
e/ x + 2x + 3x – 19 = 3x + 5
a) \(PT\Leftrightarrow3x-2x=2-3\Leftrightarrow x=-1\)
Vậy: \(S=\left\{-1\right\}\)
b) \(PT\Leftrightarrow-2x+3x=-7+22\Leftrightarrow x=15\)
Vậy: \(S=\left\{15\right\}\)
c) \(PT\Leftrightarrow8x-5x=3+12\Leftrightarrow3x=15\Leftrightarrow x=5\)
Vậy: \(S=\left\{5\right\}\)
d) \(PT\Leftrightarrow x+4x-2x=12+25-1\Leftrightarrow3x=36\Leftrightarrow x=12\)
Vậy: \(S=\left\{12\right\}\)
e) \(PT\Leftrightarrow x+2x+3x-3x=19+5\Leftrightarrow3x=24\Leftrightarrow x=8\)
Vậy: \(S=\left\{8\right\}\)
a)3x-2=2x-3
=>x=-1
b)7-2x=22-3x
=>x=15
c)8x-3=5x+12
=>3x=15
=>x=5
d)x-12+4x=25+2x-1
=>3x=12
=>x=4
e)x+2x+3x-19=3x+5
=>3x=24
=>x=8
a)3x-2=2x-3
=>x=-1
b)7-2x=22-3x
=>x=15
c)8x-3=5x+12
=>3x=15
=>x=5
d)x-12+4x=25+2x-1
=>3x=36
=>x=12
e)x+2x+3x-19=3x+5
=>3x=24
=>x=8
Bài 3: Giải các phương trình sau:
a, 2x3 - 50x = 0
b, 2x (3x - 5) - (5 - 3x)
c, 9(3x - 2) = x(2 - 3x)
d, (2x - 1)2 - 25 = 0
e, 25x2 - 2 = 0
f, x2 - 25 = 6x - 9
g, 5x(x - 3) - 2x + 6 = 0
h, 3x(x - 7) - 2(x - 7) = 0
i, 7x2 - 28 = 0
j, (2x + 1) + x(2x + 1) = 0
k, (x + 2)2 - (x - 2)(x + 2) = 0
l, x3 + 5x2 - 4x - 20 = 0
m, x2 - 25 + 2(x + 5) = 0
n, x3 - 3x + 2 = 0
o, x2 - 6x + 8 = 0
p, x2 - 5x - 14 = 0
q, (x - 2)2 - (x - 3)(x + 3) = 6
r, (2x - 1)2 - (2x + 5)(2x - 5) = 18
Bài 1: Giải các phương trình sau:
a) 3(2,2-0,3x)=2,6 + (0,1x-4)
b) 3,6 -0,5 (2x+1) = x - 0,25(22-4x)
Bài 2: Giải các phương phương trình sau:
a) \(\dfrac{3\left(x-3\right)}{4}\)+\(\dfrac{4x-10,5}{4}\)=\(\dfrac{3\left(x+1\right)}{5}\)+6
b) \(\dfrac{2\left(3x+1\right)+1}{4}\)-5=\(\dfrac{2\left(3x-1\right)}{5}\)-\(\dfrac{3x+2}{10}\)
Mik đang cần gấp nha!!❤
Bài 1: Giải các phương trình sau:
a) 3(2,2-0,3x)=2,6 + (0,1x-4)
<=> 6.6 - 0.9x = 2,6 + 0,1x - 4
<=> - 0.9x - 0,1x = -6.6 -1,4
<=> -x = -8
<=> x = 8
Vậy x = 8
b) 3,6 -0,5 (2x+1) = x - 0,25(22-4x)
<=> 3,6 - x - 0,5 = x - 5,5 + x
<=> - x - 3,1 = -5,5
<=> - x = -2.4
<=> x = 2.4
Vậy x = 2.4
Giải các phương trình sau:
a) \({2^x} = \frac{1}{{{2^{x + 1}}}};\)
b) \(2{e^{2x}} = 5.\)
\(a,2^{3x-1}=2^{-\left(x+1\right)}\Rightarrow3x-1=-\left(x+1\right)\Rightarrow x=\dfrac{1}{2}\)
\(b,ln\left(2e^{2x}\right)=ln5\)
\(\Rightarrow ln2+lne^{2x}=ln5\)
\(\Rightarrow ln2+2x=ln5\)
\(\Rightarrow2x=ln5-ln2=ln\dfrac{5}{2}\)
Như vậy \(x=\dfrac{1}{2}ln\dfrac{5}{2}\)
Giải các hệ phương trình sau:
a.{2x-3y = -5
{-3x + 4y = 2
b.{2x - 3y = -5
{-3x + 4y = 2
\(a,\Leftrightarrow\left\{{}\begin{matrix}6x-9y=-15\\-6x+8y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-3y=-5\\-y=-11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-5+33}{2}=14\\y=11\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}2x-3y=-5\\-3x+4y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x-9y=-15\\-6x+8y=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-y=-11\\2x-3y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=11\\x=\dfrac{-5+3y}{2}=\dfrac{-5+3\cdot11}{2}=14\end{matrix}\right.\)
Bài 1: Giải các phương trình sau:
a) 3x ^ 2 - 5x + 2 = 0
d) - 4x ^ 2 + 25 = 0
b) 11x - 2x ^ 2 = 0
e) sqrt(x ^ 2 - x + 9) = 2x + 1
c) x ^ 2 + 5x + 7 = 0
f) 6x ^ 4 - 7x ^ 2 + 1 = 0
a: =>3x^2-3x-2x+2=0
=>(x-1)(3x-2)=0
=>x=2/3 hoặc x=1
b: =>2x^2=11
=>x^2=11/2
=>\(x=\pm\dfrac{\sqrt{22}}{2}\)
c: Δ=5^2-4*1*7=25-28=-3<0
=>PTVN
f: =>6x^4-6x^2-x^2+1=0
=>(x^2-1)(6x^2-1)=0
=>x^2=1 hoặc x^2=1/6
=>\(\left[{}\begin{matrix}x=\pm1\\x=\pm\dfrac{\sqrt{6}}{6}\end{matrix}\right.\)
d: =>(5-2x)(5+2x)=0
=>x=5/2 hoặc x=-5/2
e: =>4x^2+4x+1=x^2-x+9 và x>=-1/2
=>3x^2+5x-8=0 và x>=-1/2
=>3x^2+8x-3x-8=0 và x>=-1/2
=>(3x+8)(x-1)=0 và x>=-1/2
=>x=1
giải các phương trình sau:
a) \(x^2+4x+5=2\sqrt{2x+3}\).
b) \(3x^2+2x=2\sqrt{x^2+x}+1-x\).
\(a,\Leftrightarrow x^2+2x+1+2x+3-2\sqrt{2x+3}+1=0\\ \Leftrightarrow\left(x+1\right)^2+\left(\sqrt{2x+3}-1\right)^2=0\\ \Leftrightarrow\left\{{}\begin{matrix}x=-1\\2x+3=1\end{matrix}\right.\Leftrightarrow x=-1\left(N\right)\)
\(b,\Leftrightarrow3x^2+3x-2\sqrt{x^2+x}=0\left(x\le-1;x\ge0\right)\\ \Leftrightarrow3x\left(x-1\right)-2\sqrt{x\left(x+1\right)}=0\\ \Leftrightarrow\sqrt{x\left(x+1\right)}\left(3\sqrt{x\left(x-1\right)}-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x\left(x-1\right)=0\\\sqrt{x\left(x-1\right)}=\dfrac{2}{3}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x^2-x-\dfrac{4}{9}=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\9x^2-9x-4=0\left(1\right)\end{matrix}\right.\)
\(\Delta\left(1\right)=81-4\left(-4\right)\cdot9=225\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=\dfrac{9-15}{18}\\x=\dfrac{9+15}{18}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(N\right)\\x=1\left(N\right)\\x=-\dfrac{1}{3}\left(L\right)\\x=\dfrac{4}{3}\left(N\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=\dfrac{4}{3}\end{matrix}\right.\)