Question

[Đặng Thị Cẩm Tú]

Tìm x, biết

a. \(\left(x+2\right)^2=81\)

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

Answer 1

[Aki Tsuki]

a/ \(\left(x+2\right)^2=81\)

\(\Rightarrow\left(x+2\right)^2=9^2;\left(x+2\right)^2=\left(-9\right)^2\)

+) \(x+2=9\)

\(\Rightarrow x=7\)

+) \(x+2=-9\)

\(\Rightarrow x=-11\)

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

\(\Rightarrow5^x+5^x.5^2=650\)

\(\Rightarrow5^x\left(25+1\right)=650\)

\(\Rightarrow5^x=\frac{650}{26}=25\)

\(\Rightarrow5^x=5^2\)

\(\Rightarrow x=2\)

Answer 2

[Nghiêm Gia Phương]

a) \(\left(x+2\right)^2=81\)

\(\Rightarrow\left(x+2\right)^2=\left(\pm9\right)^2\)

\(\Rightarrow x+2=\pm9\)

\(\Rightarrow\left[\begin{matrix}x+2=-9\\x+2=9\end{matrix}\right.\) \(\Rightarrow\left[\begin{matrix}x=-9-2\\x=9-2\end{matrix}\right.\) \(\Rightarrow\left[\begin{matrix}x=-11\\x=7\end{matrix}\right.\)

Vậy \(x=-11\) hoặc \(x=7\) thì thỏa mãn đề bài.

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

\(\Rightarrow5^x+5^x\times5^2=650\)

\(\Rightarrow5^x\times\left(1+5^2\right)=650\)

\(\Rightarrow5^x\times\left(1+25\right)=650\)

\(\Rightarrow5^x\times26=650\)

\(\Rightarrow5^x=650\div26\)

\(\Rightarrow5^x=25\)

\(\Rightarrow5^x=5^2\)

\(\Rightarrow x=2\)

Vậy \(x=2\) thì thỏa mãn đề bài.