Question

[Nam Lee]

Tìm x biết :

a) ( 2x - 1 )³ = ( 2x - 1 )⁴ .

b) ( 2017 )^{x + 2} = ( 2018 - 5³ )^{x + 2} .

c) 5^{x + 2} + 5^x = 650 .

d) 81^x = ( -3 )⁷

Answer 1

[Akai Haruma]

c) \(5^{x+2}+5^x=650\)

\(\Leftrightarrow 5^x(5^2+1)=650\)

\(\Leftrightarrow 5^x.26=650\)

\(\Rightarrow 5^x=25=5^2\Rightarrow x=2\)

d) \(81^x=(-3)^7\)

Ta thấy \(81^x>0, \forall x\in\mathbb{R}\)

\((-3)^7<0\)

Do đó pt đã cho vô nghiệm.

Answer 2

[Akai Haruma]

Lời giải:

a) \((2x-1)^3=(2x-1)^4\)

\(\Leftrightarrow (2x-1)^4-(2x-1)^3=0\)

\(\Leftrightarrow (2x-1)^3[(2x-1)-1]=0\)

\(\Leftrightarrow (2x-1)^3(2x-2)=0\)

\(\Rightarrow \left[\begin{matrix} 2x-1=0\\ 2x-2=0\end{matrix}\right.\Rightarrow \left[\begin{matrix} x=\frac{1}{2}\\ x=1\end{matrix}\right.\)

b) \(2017^{x+2}=(2018-5^3)^{x+2}\)

\(\Rightarrow \left[\begin{matrix} x+2=0(1)\\ 2017=2018-5^3(2)\end{matrix}\right.\)

(1)\(\Rightarrow x=-2\)

(2): hiển nhiên vô lý

Vậy pt có nghiệm $x=-2$