\(Cho:x+y=2.CMR:x^{2017}+y^{2017}\le x^{2018}+y^{2018}\)

Nung nóng 170 kg đá vôi thu được 84 kg vôi sống và 66 kg khí cacbonic. Tính khối lượng đá vôi đem nung - Tính khối lượng tạp chất và % tạp chất.

\(b) x^2 -5x+4=0 \)

\(<=> x^2 -4x-x+4 =0 \)

\(<=> (x^2-x)-(4x-4)=0\)

\(<=> x(x-1)-4(x-1)=0 \)

\(<=> (x-1)(x-4)=0\)

<=>\(\left[{}\begin{matrix}x-1=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\end{matrix}\right.\)

Vậy x = 1 hoặc x = 4

c) \(3x(x-5) = 60+15x+3x^2\)

\(<=> 3x^2 -15x = 60 +15x+3x^2\)

\(<=> 3x^2 - 3x^2-15x-15x=60 \)

\(<=> 30x = 60 <=> x = 60 : 30 = 2 \)

=> \(\dfrac{4\left(a-b\right)}{5\left(a+b\right)}x=\dfrac{\left(a-b\right)\left(a+b\right)}{\left(a+b\right)^2}\)

=> \(\dfrac{4}{5}.\dfrac{a-b}{a+b}x=\dfrac{a-b}{a+b}\)

=> \(\dfrac{4}{5}x=1\)

=> \(x=\dfrac{5}{4}\)

Đặt 2005 = x +1 . Ta có :

x⁶ - (x + 1 )x⁵ + ( x + 1 )x⁴ - (x + 1 )x³ + ( x + 1 )x² - (x + 1)x + (x + 1)

= x⁶ - x⁶ - x⁵ + x⁵ + x⁴ - x⁴ - x³ + x³ + x² - x² -x + x + 1

= 1

a) 15 - 3x = 6

=> 3x = 15 - 6

=> 3x = 9

=> x = 9 : 3 = 3

b) \(\dfrac{2}{3}-\dfrac{4}{3}x=\dfrac{1}{2}\Rightarrow\dfrac{4}{3}x=\dfrac{2}{3}-\dfrac{1}{2}\Rightarrow\dfrac{4}{3}x=\dfrac{1}{6}\Rightarrow x=\dfrac{1}{6}:\dfrac{4}{3}\Rightarrow x=\dfrac{3}{24}=\dfrac{1}{8}\)c) 3¹⁹.(x - 12 ) = 4 . 3²⁰

^{=> x - 12 = 4 . 3}

^{=> x - 12 = 12}

^{=> x = 12 + 12 = 24}

^{d) 3.(x - 4) = 2^2 . 3^3}

^{=> x - 4 = 2^2 . 3^2}

^{=> x - 4 = 36}

^{=> x = 36 + 4 = 40}

\(\dfrac{x-3}{x+5}=\dfrac{5}{7}\)

\(=> (x-3).7 = (x+5).5 \)

\(=> 7x-21 = 5x + 25 \)

\( => 7x -5x = 25+21 \)

\( => 2x = 46 \)

\( => x = 46 : 2 = 23\)

\(T=\left(\dfrac{1}{2}+1\right).\left(\dfrac{1}{3}+1\right).\left(\dfrac{1}{4}+1\right).......\left(\dfrac{1}{98}+1\right).\left(\dfrac{1}{99}+1\right) \) \(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}....\dfrac{99}{98}\cdot\dfrac{100}{99}\)

\(=\dfrac{100}{2}=50\)