Question

a) x²-5x=0

b)x⁴=125x

c)3^x+3^x+2=90

Answer 1

a) \(x^2-5x=0\)

\(x\left(x-5\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x-5=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=5\end{cases}}}\)

b) \(x^4=125x\)

\(x^4-125x=0\)

\(x\left(x^3-125\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x^3-125=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=5\end{cases}}}\)

c) \(3^x+3^{x+2}=90\)

\(3^x\left(1+3^2\right)=90\)

\(3^x\cdot10=90\)

\(3^x=9=3^2\)

\(\Rightarrow x=2\)

Answer 2

a) x² - 5x  = 0

x.(x-5) = 0

=> x = 0

x-5 = 0 => x = 5

KL:...

b) x⁴ = 125x

=> x³ = 125 = 5³

=> x = 5

c) 3^x + 3^x+2 = 90

3^x + 3^x.9 = 90

3^x.(1+9) = 90

3^x.10 = 90

3^x = 9 = 3²

=> x = 2

Answer 3

     \(x^2-5x=0\)

\(\Rightarrow x\left(x-5\right)=0\Rightarrow\orbr{\begin{cases}x=0\\x=5\end{cases}}\)

     \(x^4=125x\)

\(\Rightarrow x^4-125x=0\)

\(\Rightarrow x\left(x^3-125\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x^3=125\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x^3=5^3\end{cases}\Rightarrow}}\orbr{\begin{cases}x=0\\x=5\end{cases}}\)

     \(3^x+3^{x+2}=90\)

\(\Rightarrow3^x+3^x.3^2=90\)

\(\Rightarrow3^x\left(3^2+1\right)=90\)

\(\Rightarrow3^x.10=90\)

\(\Rightarrow3^x=9\Rightarrow3^x=3^2\Rightarrow x=2\)

Answer 4

a)Ta có: TH1:x khác 0 x^2=5x=>x=5

TH2 x=0

b) x^3=125=>x=5

c)3^x+3^x*9=90=>3^x*10=90=>3^x=9=>x=3

Answer 5

\(a.x^2-5x=0\text{ }\Leftrightarrow x\cdot\left(x-5\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x-5=0\Leftrightarrow x=0+5=5\end{cases}}\)

\(b.x^4=125x\Leftrightarrow x^4-125x=0\Leftrightarrow x\cdot\left(x^3-125\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x^3-125=0\Leftrightarrow x^3=125\Leftrightarrow x=5\end{cases}}\)

\(c.3^x+3^{x+2}=90\)

\(\Leftrightarrow3^x+3^x\cdot3^2=90\)

\(\Leftrightarrow3^x\cdot\left(1+9\right)=90\)

\(\Leftrightarrow3^x\cdot10=90\)

\(\Leftrightarrow3^x=90:10\)

\(\Leftrightarrow3^x=9\Leftrightarrow x=2\)