Question

x.(x-2)= 16; 2 mũ x+3.2 mũ x=144

Answer 1

\(x\)(\(x\) - 2) = 16

\(x^2\) - 2\(x\) - 16 = 0

(\(x^2\) - \(x\)) - (\(x\) - 1) - 17 = 0

\(x\)(\(x\) - 1) - (\(x-1\)) = 17

(\(x\) - 1)(\(x\) - 1) = 17

(\(x-1\))² = 17

\(\left[{}\begin{matrix}x-1=\sqrt{17}\\x-1=-\sqrt{17}\end{matrix}\right.\)

\(\left[{}\begin{matrix}x=1+\sqrt{17}\\x=1-\sqrt{17}\end{matrix}\right.\)

Vậy: \(\in\) {1 - \(\sqrt{17}\); 1 + \(\sqrt{17}\)}

 

 

 

Answer 2

Bài 2:

2^\(x\) + 3.2^\(x\) = 144

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

2^\(x\).4 = 144

2^\(x\) = 144 : 4

2^\(x\) = 36

2\(^x\) = 36

Nếu \(x\) = 6 ⇒ 2\(^x\) = 64 > 36 (loại)

Nếu \(x\) ≤ 5 ⇒2\(^x\) ≤ 2⁵ = 32 < 36 (loại)

Vậy \(x\in\) \(\varnothing\)