║x+3/4 ║-3/4=1/3 2 mũ 3x+2=4x+5 (3x-5/12)mũ 2-121/64=0 20/07/2021 Bởi Amara ║x+3/4 ║-3/4=1/3 2 mũ 3x+2=4x+5 (3x-5/12)mũ 2-121/64=0
a) `|x+3/4|-3/4=1/3` Với `x+3/4<0` hay `x<-3/4` thì `|x+3/4|=-x-3/4` `→-x-3/4-3/4=1/3` `→-x-3/2=1/3` `→-x=1/3+3/2` `→-x=11/6` `→x=-11/6` (Thỏa mãn) Với `x+3/4≥0` hay `x≥-3/4` thì `|x+3/4|=x+3/4` `→x+3/4-3/4=1/3` `→x=1/3` (Thỏa mãn) Vậy `x∈{-11/6;1/3}` b) `2^3x+2=4x+5` `→8x+2=4x+5` `→4x=3` `→x=3/4` Vậy `x=3/4` c) `(3x-5/12)^2-121/64=0` `→(3x-5/12)^2=121/64` `→`\(\left[ \begin{array}{l}3x-\dfrac{5}{12}=\dfrac{11}{8}\\3x-\dfrac{5}{12}=\dfrac{-11}{8}\end{array} \right.\) `→`\(\left[ \begin{array}{l}3x=\dfrac{43}{24}\\3x=\dfrac{-23}{24}\end{array} \right.\) `→`\(\left[ \begin{array}{l}x=\dfrac{43}{72}\\x=\dfrac{-23}{72}\end{array} \right.\) Vậy `x∈{43/72;-23/72}` Bình luận
Bạn xem hình:
a)
`|x+3/4|-3/4=1/3`
Với `x+3/4<0` hay `x<-3/4` thì `|x+3/4|=-x-3/4`
`→-x-3/4-3/4=1/3`
`→-x-3/2=1/3`
`→-x=1/3+3/2`
`→-x=11/6`
`→x=-11/6` (Thỏa mãn)
Với `x+3/4≥0` hay `x≥-3/4` thì `|x+3/4|=x+3/4`
`→x+3/4-3/4=1/3`
`→x=1/3` (Thỏa mãn)
Vậy `x∈{-11/6;1/3}`
b)
`2^3x+2=4x+5`
`→8x+2=4x+5`
`→4x=3`
`→x=3/4`
Vậy `x=3/4`
c)
`(3x-5/12)^2-121/64=0`
`→(3x-5/12)^2=121/64`
`→`\(\left[ \begin{array}{l}3x-\dfrac{5}{12}=\dfrac{11}{8}\\3x-\dfrac{5}{12}=\dfrac{-11}{8}\end{array} \right.\)
`→`\(\left[ \begin{array}{l}3x=\dfrac{43}{24}\\3x=\dfrac{-23}{24}\end{array} \right.\)
`→`\(\left[ \begin{array}{l}x=\dfrac{43}{72}\\x=\dfrac{-23}{72}\end{array} \right.\)
Vậy `x∈{43/72;-23/72}`