Giải phương trình:
a)\(\left(x+1\right)^2\left(x+2\right)+\left(x-1\right)^2\left(x-2\right)=12\)(nghiệm bằng 1)
b)\(\left(x-6\right)^4+\left(x-8\right)^4=16\)
Giải phương trình:
a) \(\dfrac{1}{x-2}+3=\dfrac{x-3}{2-x}\)
b) \(\dfrac{3}{\left(x-1\right)\left(x-2\right)}+\dfrac{2}{\left(x-3\right)\left(x-1\right)}=\dfrac{1}{\left(x-2\right)\left(x-3\right)}\)
c) \(1+\dfrac{1}{x+2}=\dfrac{12}{8+x^3}\)
a: =>1+3x-6=-x+3
=>3x-5=-x+3
=>4x=8
=>x=2(loại)
b: \(\Leftrightarrow\dfrac{3\left(x-3\right)+2\left(x-2\right)}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}=\dfrac{x-1}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}\)
=>3x-9+2x-4=x-1
=>5x-13=x-1
=>4x=12
=>x=3(loại)
c: =>x^2-2x+4+x^3+8=12
=>x^3+x^2-2x=0
=>x(x^2+x-2)=0
=>x(x+2)(x-1)=0
=>x=0 hoặc x=1
Giải các phương trình sau:
a \(\left(x+2\right)\left(x+\text{4}\right)\left(x+6\right)\left(x+8\right)+16=0\)
b \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=0\)
c \(\left(4x+1\right)\left(12x-1\right)\left(3x+2\right)\left(x+1\right)-4=0\)
d \(\left(x^2-3x+2\right)\left(x^2+15x+56\right)+8=0\)
b: Ta có: \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=0\)
\(\Leftrightarrow\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24=0\)
\(\Leftrightarrow\left(x^2+7x\right)^2+22\left(x^2+7x\right)+120-24=0\)
\(\Leftrightarrow x^2+7x+6=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-6\end{matrix}\right.\)
Giải các phương trình:
a) \(\left(x+2\right)^3-x+1=\left(x-1\right)\left(x+1\right)\)
b) \(\left(x+1\right)^3-x+1=\left(x-1\right)\left(x-2\right)\)
a) (x+2)3−x+1=(x−1)(x+1)
=>(x+2)(x2-2x+4)-x+1=(x2-12)
=>x3-2x2+4x+2x2-4x+8-x+1=(x2-1)
=>x3-2x2+4x+2x2-4x+8+1-x2+1=0
=>x3-x2+10=0
=>x3-x2=-10
=>x2(x-1)=-10
=>....
Giải phương trình:
a) \(\sqrt{4-3x}=8\)
b) \(\sqrt{4x-8}-12\sqrt{\dfrac{x-2}{9}}=-1\)
c) \(\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)=7\)
Sửa lại câu c) đặt \(\sqrt{x}+1=\)t \(\Rightarrow\left[2\left(t+\dfrac{1}{2}\right)\right]\left(t-3\right)\)=7⇒\(\left\{{}\begin{matrix}t=3\\t=-\dfrac{1}{2}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=4\\x=\dfrac{9}{4}\end{matrix}\right.\)
a) \(\left(\sqrt{4-3x}\right)^2=8^2\)\(\Leftrightarrow4-3x=64\Rightarrow x=-20\)
b) \(\sqrt{4x-8}+1=12\sqrt{\dfrac{x-2}{9}}\Leftrightarrow2\sqrt{x-2}+1\)\(=\left(12\sqrt{\left(x-2\right).\dfrac{1}{9}}\right)\)
\(\Leftrightarrow2t+1=12.\dfrac{1}{3}t\) (Đặt t = \(\sqrt{x-2}\))
\(\Rightarrow t=\dfrac{1}{2}\) \(\Rightarrow\sqrt{x-2}=\dfrac{1}{2}\)\(\Rightarrow x=\dfrac{9}{4}\)
c) pt\(\Leftrightarrow\left\{{}\begin{matrix}2\sqrt{x}+1=7\\\sqrt{x}-2=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x}=3\\\sqrt{x}=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=9\\x=4\end{matrix}\right.\)
a) Ta có: \(\sqrt{4-3x}=8\)
\(\Leftrightarrow4-3x=64\)
\(\Leftrightarrow3x=4-64=-60\)
hay x=-20
b) Ta có: \(\sqrt{4x-8}-12\cdot\sqrt{\dfrac{x-2}{9}}=-1\)
\(\Leftrightarrow2\cdot\sqrt{x-2}-12\cdot\dfrac{\sqrt{x-2}}{3}=-1\)
\(\Leftrightarrow-2\cdot\sqrt{x-2}=-1\)
\(\Leftrightarrow\sqrt{x-2}=\dfrac{1}{2}\)
\(\Leftrightarrow x-2=\dfrac{1}{4}\)
hay \(x=\dfrac{9}{4}\)
Giải phương trình:
a) \(x^2-\left(x+3\right)\left(3x+1\right)=9\).
b) \(x^3+4x+5=0\).
c) \(\left(x+14\right)^3-\left(x+12\right)^3=1352\).
d) \(x^3+\left(x-3\right)^3=\left(2x-3\right)^3\).
e) \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)=360\).
f) \(x^3+\left(x-2\right)\left(2x+1\right)=8\).
b) Ta có: \(x^3+4x+5=0\)
\(\Leftrightarrow x^3-x+5x+5=0\)
\(\Leftrightarrow x\left(x^2-1\right)+5\left(x+1\right)=0\)
\(\Leftrightarrow x\left(x+1\right)\left(x-1\right)+5\left(x+1\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-x+5\right)=0\)
mà \(x^2-x+5>0\forall x\)
nên x+1=0
hay x=-1
Vậy: S={-1}
a)x2-(x+3)(3x+1)=9
⇔(x-3)(x+3)-(x+3)(3x+1)=0
⇔x+3=0 hoặc 3x+1=0
1.x+3=0 ⇔x=-3
2.3x+1=0⇔x=-1/3
phương trình có 2 nghiệm x=-3 và x=-1/3
Giải các phương trình:
a) \(\left|2x\right|=x-6\)
b) \(\left|-3x\right|=x-8\)
c) \(\left|4x\right|=2x+12\)
d)\(\left|-5x\right|-16=3x\)
\(a,\left|2x\right|=x-6\)
\(\Leftrightarrow2x=x-6\)
\(\Leftrightarrow2x-x=-6\)
\(\Leftrightarrow x=-6\)
____________________
\(b,\left|-3x\right|=x-8\)
\(\Leftrightarrow3x=x-8\)
\(\Leftrightarrow3x-x=-8\)
\(\Leftrightarrow2x=-8\)
\(\Leftrightarrow x=-4\)
____________________
\(c,\left|4x\right|=2x+12\)
\(\Leftrightarrow4x=2x+12\)
\(\Leftrightarrow4x-2x=12\)
\(\Leftrightarrow2x=12\)
\(\Leftrightarrow x=6\)
____________________
\(d,\left|-5x\right|-16=3x\)
\(\Leftrightarrow5x-16=3x\)
\(\Leftrightarrow5x-3x=16\)
\(\Leftrightarrow2x=16\)
\(\Leftrightarrow x=8\)
Giải phương trình:
a) \(5x^2-10x=4\left(x-1\right)\sqrt{x^2-2x+2}\)
b) \(\sqrt{2x^2+22x+29}-x-2=2\sqrt{2x+3}\)
c) \(x^3-7x^2+9x+12=\left(x-3\right)\left(x-2+5\sqrt{x-3}\right)\left(\sqrt{x-3}-1\right)\)
Mọi người giúp gấp với ạ.
GIẢI PHƯƠNG TRÌNH:
a) \(x^2-6x-4\sqrt{x^2-6x+6}=-9\)
b) \(\left(x+1\right)\left(x+4\right)=5\sqrt{x^2+5x+28}\)
b: Đặt \(x^2+5x+4=a\)
\(\Leftrightarrow a=5\sqrt{a+24}\)
\(\Leftrightarrow a^2=25a+600\)
\(\Leftrightarrow a^2-25a-600=0\)
\(\Leftrightarrow\left(a-40\right)\left(a+15\right)=0\)
\(\Leftrightarrow a=-15\)
hay S=∅
Giải các phương trình sau:
a \(x^4-x^2-56=0\)
b \(\left(x-2\right)^4+\left(x+2\right)^4=32\)
c \(\left(x+3\right)^4+\left(x+5\right)^4=16\)
d \(\left(6-x\right)^4+\left(8-x\right)^4=80\)
a) \(x^4-x^2+\dfrac{1}{4}-\dfrac{225}{4}=0\\ \left(x^2-\dfrac{1}{2}\right)^2-\dfrac{15}{2}^2=0\\ \left(x+7\right)\left(x-8\right)=0\\ \left[{}\begin{matrix}x=8\\x=-7\end{matrix}\right.\)
Vậy x = 8 hoặc x = -7
a: Ta có: \(x^4-x^2-56=0\)
\(\Leftrightarrow x^4-8x^2+7x^2-56=0\)
\(\Leftrightarrow\left(x^2-8\right)\left(x^2+7\right)=0\)
\(\Leftrightarrow x^2-8=0\)
hay \(x\in\left\{2\sqrt{2};-2\sqrt{2}\right\}\)