`C=-2x^2+x+1`

`C=-2(x^2-x/2)+1`

`C=-2(x^2-2*x*1/4+1/16)+1+1/8`

`C=-2(x-1/4)^2+9/8<=9/8`

Dấu "=" `<=>x=1/4.`

Ta có: \(C=-2x^2+x+1\)

\(=-2\left(x^2-2\cdot x\cdot\dfrac{1}{4}+\dfrac{1}{16}-\dfrac{9}{16}\right)\)

\(=-2\left(x-\dfrac{1}{4}\right)^2+\dfrac{9}{8}\le\dfrac{9}{8}\forall x\)

Dấu '=' xảy ra khi \(x=\dfrac{1}{4}\)

`#3107`

b)

`2.3^x = 162`

`\Rightarrow 3^x = 162 \div 2`

`\Rightarrow 3^x = 81`

`\Rightarrow 3^x = 3^4`

`\Rightarrow x = 4`

Vậy, `x = 4`

c)

`(2x - 15)^5 = (2 - 15)^3`

\(\Rightarrow \)`(2x - 15)^5 - (2x - 15)^3 = 0`

\(\Rightarrow \)`(2x - 15)^3 . [ (2x - 15)^2 - 1] = 0`

\(\Rightarrow\left[{}\begin{matrix}\left(2x-15\right)^3=0\\\left(2x-15\right)^2-1=0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x-15=0\\\left(2x-15\right)^2=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}2x=15\\\left(2x-15\right)^2=\left(\pm1\right)^2\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\2x-15=1\\2x-15=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\2x=16\\2x=-14\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{15}{2}\\x=8\\x=-7\end{matrix}\right.\)

Vậy, `x \in`\(\left\{-7;8;\dfrac{15}{2}\right\}.\)

`d)`

\(3^{x+2}-5.3^x=?\) Bạn ghi tiếp đề nhé!

`e)`

\(7\cdot4^{x-1}+4^{x-1}=23?\)

\(4^{x-1}\cdot\left(7+1\right)=23\\ \Rightarrow4^{x-1}\cdot8=23\\ \Rightarrow4^{x-1}=\dfrac{23}{8}\)

Bạn xem lại đề!

`f)`

\(2\cdot2^{2x}+4^3\cdot4^x=1056\)

\(\Rightarrow2\cdot2^{2x}+\left(2^2\right)^3\cdot\left(2^2\right)^x=1056\\ \Rightarrow2\cdot2^{2x}+2^6\cdot2^{2x}=1056\\ \Rightarrow2^{2x}\cdot\left(2+2^6\right)=1056\\ \Rightarrow2^{2x}\cdot66=1056\\ \Rightarrow2^{2x}=1056\div66\\ \Rightarrow2^{2x}=16\\ \Rightarrow2^{2x}=2^4\\ \Rightarrow2x=4\\ \Rightarrow x=2\)

Vậy, `x = 2`

_____

\(10 -{[(x \div 3+17) \div 10+3.2^4] \div 10}=5\)

\(\Rightarrow\left[\left(x\div3+17\right)\div10+48\right]\div10=10-5\)

\(\Rightarrow\left[\left(x\div3+17\right)\div10+48\right]\div10=5\)

\(\Rightarrow\left(x\div3+17\right)\div10+48=50\)

\(\Rightarrow\left(x\div3+17\right)\div10=2\)

\(\Rightarrow x\div3+17=20\)

\(\Rightarrow x\div3=3\\ \Rightarrow x=9\)

Vậy, `x = 9.`

Bài 1 . Tìm x

a) 723 - ( 7x - 152 ) = 714

                7x - 152   = 723 - 714

                7x - 152   = 9

                7x            = 9 + 152

                7x            = 161

                  x            = 161 : 7

                  x            = 23

Vậy x = 23

b) ( 2x - 130 ) : 4 + 213 = 5² + 193

    ( 2x - 130 ) : 4 + 213 = 218

    ( 2x - 130 ) : 4           = 218 - 213

    ( 2x - 130 ) : 4           = 5

      2x - 130                   = 5 . 4

      2x - 130                   = 20

      2x                            = 20 + 130

      2x                            = 150

        x                            = 150 : 2

        x                            = 75

Vậy x = 75

c) ( x - 6 )² = 9

    ( x - 6 )² = 3²

      x - 6     = 3    <=>    x = 3 + 6            <=>    x = 9

      x - 6     = -3   <=>   x  = -3 + 6           <=>    x = 3

b) x^10=1x

=> x=0 ; 1

c)(2x-15)^5=(2x-15)^3

=> (2x-15)^4 = (2x-15)^2

=> (2x-15)^2 =1

=> 2x-15=1

=> x=8