tìm x:
1. (x-2) mũ 2 = 1
2. (x+1/2) mũ 2 = 1/4
3. (3x-1) mũ 3 = -8/27
4. (2x+3 )mũ 2 = 9/121
5.(2x-1)mũ 3 =27
tìm x:
1. (x-2) mũ 2 = 1
2. (x+1/2) mũ 2 = 1/4
3. (3x-1) mũ 3 = -8/27
4. (2x+3 )mũ 2 = 9/121
5.(2x-1)mũ 3 =27
`1, (x-2)² = 1`
`⇔ (x-2)² = (±1)²`
`⇔`\(\left[ \begin{array}{l}x-2=1 \\ x-2= -1\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=3\\x=1\end{array} \right.\)
`2, (x+1/2)² = 1/4`
`⇔(x+1/2)² = (±1/2)²`
`⇔`\(\left[ \begin{array}{l}x+\dfrac{1}{2}=\dfrac{1}{2} \\x+\dfrac{1}{2}=\dfrac{-1}{2}\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=0\\x=-1\end{array} \right.\)
`3, (3x-1)³ = -8/27`
`⇔(3x-1)³ = (-2/3)³`
`⇔3x-1 = -2/3`
`⇔3x = 1/3`
`⇔x = 1/9`
`4, (2x+3)² = 9/121`
`⇔(2x+3)² = (±3/11)²`
`⇔`\(\left[ \begin{array}{l}2x+3=\dfrac{3}{11} \\x+\dfrac{1}{2}=\dfrac{-1}{2}\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}2x =\dfrac{-30}{11}\\2x=\dfrac{-36}{11}\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{-15}{11}\\x=\dfrac{-18}{11}\end{array} \right.\)
`5, (2x-1)³ =27`
`⇔ (2x-1)³ = 3³`
`⇔ 2x-1=3`
`⇔ 2x=4`
`⇔ x=2`
Đáp án:
Giải thích các bước giải:
1. (x-2)² = 1
⇒(x-2)² = (±1)²
⇒x-2=1 ⇔x=3
hoặc x-2= -1 ⇔x=1
2. (x+1/2)² = 1/4
⇒(x+1/2)² = (±1/2)²
⇒x+1/2=1/2 ⇔x=0
hoặc x+1/2= -1/2 ⇔x= -1
3. (3x-1)³ = -8/27
⇒(3x-1)³ = (-2/3)³
⇒3x-1 = -2/3
⇒3x = 1/3
⇒x = 1/9
4. (2x+3)² = 9/121
⇒(2x+3)² = (±3/11)²
⇒2x+3 = 3/11 ⇔2x= -30/11 ⇔x= -15/11
hoặc 2x+3= -3/11 ⇔2x= -36/11 ⇔x= -18/11
5. (2x-1)³ =27
⇒(2x-1)³ = 3³
⇒2x-1=3
⇒2x=4
⇒x=2