Đặt A = 2007 . (144 - 1^2 )...(144 - 12^2)....(144 - 20^2)

         = 2007 . (144-1^2)...(144-144)...(144-20^2)

          = 2007 (144 - 1^2)....0 ..(144-20^2)

          = 0 

`2^(x+3)+2^x=144`

`2^x *2^3 +2^x =144`

`2^x (8+1)=144`

`2^x *9=144`

`2^x =16`

`2^x =16`

`2^x =2^4`

`=>x=4`

2\(^{x+3}\)  + 2\(^x\) = 144

2\(^x\).( 2³ + 1) = 144

2^\(x\)(8 + 1) = 144

2\(^x\) . 9 = 144

2\(^x\)       = 144 : 9

2\(^x\)       = 16

2\(^x\)        = 2⁴

 \(x\)         = 4 

\(2^x\left(1+\frac{1}{2}\right)=144\)

\(2^x=96\)

x= 6,584962501

\(144^{2015}=\left(2^4.3^2\right)^{2015}=2^{4.2015}.3^{2.2015}\)

\(\Rightarrow\left\{{}\begin{matrix}X=4.2015\\Y=2.2015\end{matrix}\right.\)

\(\left(\frac{X+Y}{X-Y}\right)^{\frac{X}{Y}}=\left(\frac{4.2015+2.2015}{4.2015-2.2015}\right)^{\frac{4.2015}{2.2015}}=\left[\frac{2015\left(4-2\right)}{2015\left(4+2\right)}\right]^{\frac{4}{2}}=\left(\frac{2}{6}\right)^2=\left(\frac{1}{3}\right)^2=\frac{1}{9}\)

\(a)2^{x+3}+2^x=144\)

\(2^x.3+2^x.1=144\)

\(2^x.\left(3+1\right)=144\)

\(2^x.4=144\)

\(2^x=144:4\)

\(2^x=36\)

\(\Rightarrow x\in\varnothing\)

phần b chịu

a, 2^x+3 + 2^x = 144

   2^x . 2³ + 2^x . 1 = 144

  2^x . ( 2³ + 1 ) = 144

  2^x . 9 = 144

        2^x = 144 : 9

         2^x = 16

         2^x = 2⁴

           x = 4

(4x-1)²=25x9

(4x-1)²=15²

=>4x-1=15

      4x     =16

(4x - 1)² = 25 . 9

\(\Rightarrow\)(4x - 1) . (4x - 1) = 225

\(\Rightarrow\)(4x - 1) . (4x - 1) = 15 . 15

\(\Rightarrow\)4x - 1 = 15

\(\Rightarrow\)4x = 16

\(\Rightarrow\)x = 4

\(4^{x-5}=16\)

\(4^{x-5}=4^2\)

\(x-5=2\)

\(x=2+5\)

\(x=7\)

\(45-2^{x-1}=29\)

\(2^{x-1}=16\)

\(2^{x-1}=2^4\)

\(x-1=4\)

\(x=5\)

\(\left(2+x\right)^2=144\)

\(\left(2+x\right)^2=12^2\)

\(2+x=12\)

\(x=12-2\)

\(x=10\)

\(\left(x-5\right)^2=81\)

\(\left(x-5\right)^2=9^2\)

\(x-5=9\)

\(x=14\)

\(\left(13-x\right)^4=81\)

\(\left(13-x\right)^4=3^4\)

\(13-x=3\)

\(x=13-3\)

\(x=10\)

\(...4^{x-5}=4^2\Rightarrow x-5=2\Rightarrow x=7\)

\(...2^{x-1}=45-29=16\Rightarrow2^{x-1}=2^4\Rightarrow x-1=4\Rightarrow x=5\)

\(...\Rightarrow\left(2+x\right)^2=12^2\Rightarrow\left[{}\begin{matrix}2+x=12\\2+x=-12\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=10\\x=-14\end{matrix}\right.\)

\(...\Rightarrow\left(x-5\right)^2=9^2\Rightarrow\left[{}\begin{matrix}x-5=3\\x-5=-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=8\\x=2\end{matrix}\right.\)

\(...\Rightarrow\left(13-x\right)^4=3^4\Rightarrow\left[{}\begin{matrix}13-x=3\\13-x=-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=10\\x=16\end{matrix}\right.\)