Question

Tìm x biết:

a) |x| + 3² = 2² + (1/2)³

b) (2x + 1)³ = - 8

c) \(5-\left|x+\frac{1}{2}\right|=2^2-\left(\frac{1}{2}\right)^3\)

Answer 1

a) |x| + 3² = 4 + 0,125

|x| + 9 = 4,125

|x| = 4,125 - 9

|x| =-4,875

Vậy x=\(\varnothing\)

Answer 2

b) (2x + 1)³ = - 8

(2x + 1)³ = (- 2)³

2x + 1 = - 2

2x = - 2 - 1

2x = -3

x = -1,5

 

Answer 3

c) 5 - |x + \(\frac{1}{2}\) = 2² - \(\left(\frac{1}{2}\right)\)³ (1)

5 - |x + \(\frac{1}{2}\) = 3,875

|x + \(\frac{1}{2}\) = 5 - 3,875

|x + \(\frac{1}{2}\) = 1,125

+ x +\(\frac{1}{2}\) > 0 \(\Rightarrow\) |x + \(\frac{1}{2}\) = x +\(\frac{1}{2}\)

(1) trở thành: x +\(\frac{1}{2}\) = 1,125

x = 0,625

+ x +\(\frac{1}{2}\) < 0 \(\Rightarrow\) |x + \(\frac{1}{2}\) = - (x +\(\frac{1}{2}\))

(1) trở thành: - (x +\(\frac{1}{2}\)) = 1,125

x +\(\frac{1}{2}\) = - 1,125

x = -1,125 -\(\frac{1}{2}\)

x = -1,625

 

 

 

 

Answer 4

\(a.\)

\(\left|x\right|+3^2=2^2+\left(\frac{1}{2}\right)^3\)

\(\Rightarrow\left|x\right|+9=4+0,125\)

\(\Rightarrow\left|x\right|+9=4,125\)

\(\Rightarrow\left|x\right|=4,125-9\)

\(\Rightarrow\left|x\right|=-4,875\)

\(\Rightarrow x\in\varnothing\)

\(b.\)

\(\left(2x+1\right)^3=-8\)

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

\(\Rightarrow2x+1=-2\)

\(\Rightarrow2x=-2-1=-3\)

\(\Rightarrow x=-\frac{3}{2}\)

\(c.\)

\(5-\left|x+\frac{1}{2}\right|=2^2-\left(\frac{1}{2}\right)^3\)

\(\Rightarrow5-\left|x+\frac{1}{2}\right|=4-\frac{1}{8}\)

\(\Rightarrow5-\left|x+\frac{1}{2}\right|=3,875\)

\(\Rightarrow\left|x+\frac{1}{2}\right|=5-3,875=1,125\)

\(\Rightarrow\left[\begin{array}{nghiempt}x+\frac{1}{2}=1,125\\x+\frac{1}{2}=-1,125\end{array}\right.\)

\(\Rightarrow\left[\begin{array}{nghiempt}x=0,625\\x=-1,625\end{array}\right.\)