Ta có: `A` lớn nhất `<=> (2015)/(18+12|x-6|)` nhỏ nhất.
`<=> 18+12|x-6|` nhỏ nhất.
`<=> 12|x-6|` nhỏ nhất, do `18` là hằng.
`<=> 12|x-6|=0`
`<=> x=6 => A=2015/18`
Vậy...
`b, B>=x+1/3+1-x`
`=4/3`.
Đẳng thức xảy ra `<=> x+1/3=1-x`
`<=> x=2/3`.
Vậy...
Bài 1: Tìm Max:
a) A= \(\dfrac{32}{x^2+2}\)
b) B= \(\dfrac{5}{2.\left(x+1\right)^2+3}\)
Tìm x, biết:
\(\)|x+\(\dfrac{1}{2}\)|+|x+\(\dfrac{1}{6}\)|+\(\left|x+\dfrac{1}{12}\right|\)+\(\left|x+\dfrac{1}{20}\right|\)+...+\(\left|x+\dfrac{1}{110}\right|\)=11x
Tìm x, biết:
a) \(\dfrac{-3}{2}x+\dfrac{1}{4}=\dfrac{1}{2}\left(x+1\right)\)
b) \(\left(6-3\sqrt{x}\right)\left(\left|x\right|-7\right)=0\)
Tìm x, biết:
a) \(-\dfrac{2}{3}\left(x+1\right)=\dfrac{1}{6}-x\)
b) \(3\left(x+\dfrac{1}{3}\right)-\dfrac{1}{2}\left(x+2\right)=\dfrac{5}{2}x-1\)
Tìm x
\(a,3-x=x+1,8\)
\(b,2x-5=7x+35\)
\(c,2\left(x+10\right)=3\left(x-6\right)\)
\(d,8\left(x-\dfrac{3}{8}\right)+1=6\left(\dfrac{1}{6}+x\right)+x\)
\(e,\dfrac{2}{9}-3x=\dfrac{4}{3}-x\)
\(g,\dfrac{1}{2}x+\dfrac{5}{6}=\dfrac{3}{4}x-\dfrac{1}{2}\)
\(h,x-4=\dfrac{5}{6}\left(6-\dfrac{6}{5}x\right)\)
\(k,7x^2-11=6x^2-2\)
\(m,5\left(x+3.2^3\right)=10^2\)
\(n,\dfrac{4}{9}-(\dfrac{1}{6^2})=\dfrac{2}{3}\left(x-\dfrac{2}{3}\right)^2+\dfrac{5}{12}\)
Bài 2: Tìm x,y,z biết:
a)\(\left(x-1\right)\)\(:\)\(\dfrac{2}{3}\)=\(\dfrac{-2}{5}\)
b) \(\left|x-\dfrac{1}{2}\right|-\dfrac{1}{3}=0\)
c) \(\left|4x+2\right|=\left|6+2x\right|\)
Tìm x :
1) \(\left(-0,75x+\dfrac{5}{2}\right).\dfrac{4}{7}-\left(-\dfrac{1}{3}\right)=-\dfrac{5}{6}\)
2) \(\left(4x-9\right)\left(2,5+\dfrac{-7}{3}x\right)=0\)
3) \(\left|x-\dfrac{3}{4}\right|-\dfrac{1}{2}=0\)
4)\(\left(\dfrac{3}{5}-\dfrac{2}{3}x\right)^3=\dfrac{-64}{125}\)
tìm x biết:
a) \(5^x.\left(5^3\right)^2=625\)
b)\(\left(\dfrac{12}{15}\right)^x=\left(\dfrac{5}{3}\right)^{-5}-\left(-\dfrac{3}{5}\right)^4\)
c)\(\left(-\dfrac{3}{4}\right)^{3x-1}=\dfrac{256}{81}\)
d)\(172x^2-7^9:98^3=2^{-3}\)
tìm x:
\(a,5^x.\left(5^2\right)^3=625\)
\(b,\left(\dfrac{12}{15}\right)^x=\left(\dfrac{5}{4}\right)^{-2}-\left(\dfrac{-3}{5}\right)^4\)
\(c,\left(\dfrac{-3}{4}\right)^{3x-1}=\dfrac{256}{81}\)
\(d,172x^2-7^9:98^3=2^{-3}\)
