Đáp án:
↓↓↓
Giải thích các bước giải:
a) |2(x+1)-(-5)|=|-2017|
|2(x+1)+5|= 2017
\(\left[ \begin{array}{l}2(x+1)+5 = 2017\\2(x+1)+5 = -2017\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}2(x+1) = 2012\\2(x+1) = -2022\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x+1 = 1006\\x+1 = -1011\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x = 1005\\x = -1012\end{array} \right.\)
b) 2(2x-1)² + |-2016|=|2066|
`2(2x-1)² + 2016 = 2066`
`2(2x-1)² = 2066-2016`
`2(2x-1)² = 50`
`(2x-1)² = 25`
`(2x+1)² = (±5)²`
⇔ \(\left[ \begin{array}{l}2x-1 = 5\\2x-1 = -5\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}2x = 6\\2x-1 = -4\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x = 3\\x = -2\end{array} \right.\)
c) `2{ 3+2[(3-2(x-1))²+1]} = 14`
`2{ 3+2[(3-2x+2)²+1} = 14`
`2{ 3+2[(5-2x)²+1} = 14`
`2[ 3+2(5-2x)²+2] = 14`
`2[5+2(5-2x)²] =14`
`10+4(5-2x)² = 14`
`4(5-2x)² = 14-10`
`4(5-2x)² = 4`
` (5-2x)² = 1`
`(5-2x)² = (±1)²`
⇔ \(\left[ \begin{array}{l}5-2x = 1\\5-2x = -1\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}-2x = -4\\-2x = -6\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x = 2 \\x = 3\end{array} \right.\)
