Question

Tìm x biết

a, |x—3|=5

b, (x+2)²=81

c, 5^x+5^x+2=650

Answer 1

a) |x-3|=5

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

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

Vậy x\(\in\){-2;8}

b) (x+2)²=81

(x+2)²=9²

\(\Rightarrow\)x+2=9

x=9-2

x=7

Vậy x=7.

c) 5^x+5^x+2=650

5^x+5^x.5²=650

5^x(1+5²)=650

5^x.26=650

5^x=650:26

5^x=25

5^x=5²

\(\Rightarrow\)x=2

Vậy x=2.

Answer 2

a) \(\left|x-3\right|=5\\ \Rightarrow\left[{}\begin{matrix}x-3=5\\x-3=-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=8\\x=-2\end{matrix}\right.\)Vậy \(x\in\left\{8;-2\right\}\)

b) \(\left(x+2\right)^2=81\\ \left(x+2\right)^2=9^2=\left(-9\right)^2\\ \Rightarrow\left[{}\begin{matrix}x+2=9\\x+2=-9\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=7\\x=-11\end{matrix}\right.\)Vậy \(x\in\left\{7;-11\right\}\)

c) \(5^x+5^{x+2}=650\\ 5^x\left(1+5^2\right)=650\\ 5^x\cdot26=650\\ 5^x=25\\ \Rightarrow x=2\)Vậy x = 2

Answer 3

\( a)\left| {x - 3} \right| = 5\\ \Leftrightarrow \left[ \begin{array}{l} x - 3 = 5\\ x - 3 = - 5 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = 8\\ x = - 2 \end{array} \right.\\ b){\left( {x + 2} \right)^2} = 81\\ \Leftrightarrow x + 2 = \pm 9\\ \Leftrightarrow \left[ \begin{array}{l} x + 2 = 9\\ x + 2 = - 9 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} x = 7\\ x = - 11 \end{array} \right.\\ c){5^x} + {5^{x + 2}} = 650\\ \Leftrightarrow \left( {1 + {5^2}} \right){5^x} = 650\\ \Leftrightarrow {26.5^x} = 650\\ \Leftrightarrow {5^x} = 25\\ \Leftrightarrow {5^x} = {5^2}\\ \Leftrightarrow x = 2 \)