a: \(\left(x+10\right)\left(x-5\right)=0\)

=>\(\left[{}\begin{matrix}x+10=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-10\\x=5\end{matrix}\right.\)

b: \(\left(2x+10\right)\left(4+x\right)=0\)

=>\(\left[{}\begin{matrix}2x+10=0\\4+x=0\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=-4\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=-5\end{matrix}\right.\)

c: \(\left(4x+20\right)\left(12x-24\right)=0\)

=>\(\left[{}\begin{matrix}4x+20=0\\12x-24=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=-20\\12x=24\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)

d: \(\left(x-2024\right)\left(4x+4\right)=0\)

=>\(\left[{}\begin{matrix}x-2024=0\\4x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2024\\4x=-4\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=-1\\x=2024\end{matrix}\right.\)

e: \(\left(2x-6\right)\left(7+x\right)=0\)

=>\(\left[{}\begin{matrix}2x-6=0\\x+7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\x=-7\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=3\\x=-7\end{matrix}\right.\)

g: (4x+8)(6-x)=0

=>\(\left[{}\begin{matrix}4x+8=0\\6-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x=6\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=-2\\x=6\end{matrix}\right.\)

h: (2x+2)(4x-8)=0

=>2(x+1)*4*(x-2)=0

=>(x+1)(x-2)=0

=>\(\left[{}\begin{matrix}x+1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)

i: (2x-2024)(8x-16)=0

=>\(2\left(x-1012\right)\cdot8\cdot\left(x-2\right)=0\)

=>\(\left(x-1012\right)\left(x-2\right)=0\)

=>\(\left[{}\begin{matrix}x-1012=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1012\\x=2\end{matrix}\right.\)

k: \(\left(4x-16\right)\left(-72+9x\right)=0\)

=>\(4\cdot\left(x-4\right)\cdot9\left(x-8\right)=0\)

=>\(36\left(x-4\right)\left(x-8\right)=0\)

=>\(\left(x-4\right)\left(x-8\right)=0\)

=>\(\left[{}\begin{matrix}x-4=0\\x-8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=8\end{matrix}\right.\)

m: \(\left(20+5x\right)\left(4x-8\right)=0\)

=>\(5\cdot\left(x+4\right)\cdot4\left(x-2\right)=0\)

=>\(\left(x+4\right)\left(x-2\right)=0\)

=>\(\left[{}\begin{matrix}x+4=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=2\end{matrix}\right.\)

n: \(\left(-4x+48\right)\left(2x-24\right)=0\)

=>\(-4\left(x-12\right)\cdot2\left(x-12\right)=0\)

=>\(\left(x-12\right)^2=0\)

=>x-12=0

=>x=12

o: \(\left(4x+16\right)\left(-2x+20\right)\left(-40+x\right)=0\)

=>\(4\cdot\left(x+4\right)\cdot\left(-2\right)\left(x-10\right)\left(x-40\right)=0\)

=>\(\left(x+4\right)\left(x-10\right)\left(x-40\right)=0\)

=>\(\left[{}\begin{matrix}x+4=0\\x-10=0\\x-40=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-4\\x=10\\x=40\end{matrix}\right.\)

p: \(\left(-5x+40\right)\left(-x+2023\right)\left(2x-2\right)=0\)

=>\(-5\left(x-8\right)\cdot\left(-1\right)\cdot\left(x-2023\right)\cdot2\left(x-1\right)=0\)

=>\(\left(x-8\right)\left(x-2023\right)\left(x-1\right)=0\)

=>\(\left[{}\begin{matrix}x-8=0\\x-1=0\\x-2023=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=1\\x=2023\end{matrix}\right.\)

q: \(2024x\left(4x-8\right)\left(5+5x\right)=0\)

=>\(x\cdot4\left(x-2\right)\cdot5\left(x+1\right)=0\)

=>\(x\left(x-2\right)\left(x+1\right)=0\)

=>\(\left[{}\begin{matrix}x=0\\x-2=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-1\end{matrix}\right.\)

r: \(-4x\left(3x+9\right)\left(2x-16\right)=0\)

=>\(-4x\cdot3\left(x+3\right)\cdot2\left(x-8\right)=0\)

=>\(x\left(x+3\right)\left(x-8\right)=0\)

=>\(\left[{}\begin{matrix}x=0\\x+3=0\\x-8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\\x=8\end{matrix}\right.\)

s: \(\left(-100+5x\right)\left(2x-10\right)\left(6x+6\right)=0\)

=>\(5\cdot\left(x-20\right)\cdot2\left(x-5\right)\cdot6\left(x+1\right)=0\)

=>\(\left(x-20\right)\left(x-5\right)\left(x+1\right)=0\)

=>\(\left[{}\begin{matrix}x-20=0\\x-5=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=20\\x=5\\x=-1\end{matrix}\right.\)

t: \(\left(-2x+4\right)\left(2x+16\right)\cdot\left(7-x\right)=0\)

=>\(-2\left(x-2\right)\cdot2\left(x+8\right)\cdot\left(-1\right)\cdot\left(x-7\right)=0\)

=>\(\left(x-2\right)\left(x+8\right)\left(x-7\right)=0\)

=>\(\left[{}\begin{matrix}x-2=0\\x-7=0\\x+8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-8\\x=7\end{matrix}\right.\)

=>x:3=472

hay x=1416

có ai lm đc bài này khum giúp mọi vs

1000-(x:3)=528 

x:3=1000-528

x:3=472

x=472x3

x=1416

2:

a: pi/2<a<pi

=>cosa<0

sin^2a+cos^2a=1

=>cos^2a=1-4/9=5/9

=>cosa=-căn 5/3

cos2a=2*cos^2a-1=2*5/9-1=10/9-1=1/9

sin(2a-pi/6)

=sin2a*cospi/6-cos2a*sinpi/6

=2*sina*cosa*(căn 3/2)-1/9*1/2

\(=2\cdot\dfrac{2}{3}\cdot\dfrac{-\sqrt{5}}{3}\cdot\dfrac{\sqrt{3}}{2}-\dfrac{1}{18}=\dfrac{-4\sqrt{15}-1}{18}\)

b; tan a=2

=>sin a=2*cosa

\(A=\dfrac{3\cdot\left(2\cdot cosa\right)^2-cos^2a+2}{5\cdot\left(2\cdot cosa\right)^2+3cosa\cdot2cosa}\)

\(=\dfrac{12\cdot cos^2a-cos^2a+2}{20cos^2a+6cos^2a}\)

\(=\dfrac{11cos^2a+2\left(4cos^2a+cos^2a\right)}{26cos^2a}=\dfrac{21}{26}\)

4:

a: (C): x^2+y^2-4x+2y-4=0

=>x^2-4x+4+y^2+2y+1=9

=>(x-2)^2+(y+1)^2=9

=>I(2;-1); R=3

b: Gọi (d) là phương trình cần tìm

(d)//4x+3y-1=0

=>(d): 4x+3y+c=0

I(2;-1);R=3

Theo đề, ta có: d(I;(d))=R=3

=>\(\dfrac{\left|4\cdot2+3\cdot\left(-1\right)+c\right|}{\sqrt{4^2+3^2}}=3\)

=>|c+5|=15

=>c=10 hoặc c=-20

x : 3 dư 2

x : 5 dư 1

→ x + 4 chia hết cho 3 và 5

→ x + 4 € BC ( 3, 5 )

Ta có: 3 . 5 = 15

→ BC ( 3, 5 ) = B ( 15 ) = {0;15;30;45;...}

Dựa vào các điều kiện trên, ta kết luận: Vậy x € { 15;30 }

đk : x>= 1 

Q = \(\sqrt{x-1}-12\)

với \(x\ge1\Leftrightarrow x-1\ge0\Leftrightarrow\sqrt{x-1}\ge0\Leftrightarrow\sqrt{x-1}-12\ge12\)

Dấu ''='' xảy ra khi x = 1