Toán Lớp 6: a) ( 2x + 3) ³=1
b) (2x + 3) ²=1
c) ( 2x – 1) ²=25
d) 4 ( x + 1 ) ²=36
e) 5 ( x – 3) ²=45
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Toán Lớp 6: a) ( 2x + 3) ³=1
b) (2x + 3) ²=1
c) ( 2x – 1) ²=25
d) 4 ( x + 1 ) ²=36
e) 5 ( x – 3) ²=45
Comments ( 2 )
a) ( 2x + 3 )^3 = 1
⇒ 2x + 3 = 1
⇒ 2x = 1 – 3
⇒ 2x = -2
⇒ x = -1
b) ( 2x + 3 )^2 = 1
⇒ $\left[\begin{matrix} 2x + 3 = -1\\ 2x + 3 = 1\end{matrix}\right.$
⇒ $\left[\begin{matrix} 2x = 2\\ 2x = -2 \end{matrix}\right.$
⇒ $\left[\begin{matrix} x = 1\\ x = -1 \end{matrix}\right.$
c) ( 2x – 1 )^2 = 25
⇒ $\left[\begin{matrix} 2x – 1 = -5\\ 2x-1 = 5\end{matrix}\right.$
⇒ $\left[\begin{matrix} 2x = -4\\ 2x = 6 \end{matrix}\right.$
⇒ $\left[\begin{matrix} 2x = -2\\ 2x = 3 \end{matrix}\right.$
d) 4 ( x + 1 )^2 =36
⇒ ( x + 1 )^2 = 36 : 4
⇒ ( x + 1 )^2 = 9
⇒ x + 1 = 3
⇒ x = 3 – 1
⇒ x = 2
e) 5 ( x – 3)^2 = 45
⇒ ( x – 3 )^2 = 45 : 5
⇒ ( x – 3 )^2 = 9
⇒ x – 3 = 3
⇒ x = 3 + 3
⇒ x = 6
Giải đáp:
$a) (2x+3)^3=1$
$⇒ (2x+3)^3=1^3$
$⇒ 2x+3=1$
$⇒ 2x=-2$
$⇒ x=-1$
$Vậy$ $x=-1$
$b) (2x+3)^2=1$
$⇒ (2x+3)^2=1^2$
$⇒ 2x+3=1$
$⇒ 2x=-2$
$⇒ x=-1$
$Vậy$ $x=-1$
$c) (2x-1)^2=25$
$⇒ (2x-1)²= (±5)²$
$\text{*Xét:}$
$TH1: 2x-1=5$
$⇒ 2x=6$
$⇒ x=3$
$TH2: 2x-1=-5$
$⇒ 2x=-4$
$⇒ x=-2$
$\text{Vậy x ∈ {3;-2}}$
$d) 4.(x+1)²=36$
$⇒ (x+1)²= 36:4$
$⇒ (x+1)^2= 9$
$⇒ (x+1)^2= (±3)²$
$\text{*xét:}$
$TH1:x+1=3$
$⇒ x=2$
$TH2: x+1=-3$
$⇒ x=-4$
$\text{Vậy x ∈ {2;-4}}$
$e) 5.(x-3)^2= 45$
$⇒ (x-3)^2= 45:5$
$⇒ (x-3)^2=9$
$⇒ (x-3)^2= (±3)^2$
$\text{*Xét:}$
$TH1: x-3=3$
$⇒ x=6$
$TH2: x-3=-3$
$⇒ x=0$
$\text{Vậy x ∈ {6;0}}$