Bài 14: tìm x
a) 8/2-|7/9-x|=-1/5
b) (x-1/4)^2-25/64=0
c) (x-1/4)^2+17/64=21/32
d) 2/5.x+1/3=1/5
e) 4/9-5/3.x=-2
f) 5/7:x-3= -2/7
bài 15: tính A= 3/1.3+3/3.5+3/5.7+…..+3/199.201
B= 5/1.3+5/3.5+5/5.7+…..+5/201.203
Mk hết điểm r mn thông cảm lm hết giúp mk nha
Đáp án:
Giải thích các bước giải:
Bài 14
a ta có 8/2-|7/9-x|=-1/5
8/2+1/5=|7/9-x|
40/10+2/10=|7/9-x|
21/5=|7/9-x|
⇒\(\left[ \begin{array}{l}7/9-x=21/5\\7/9-x=-21/5\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=-154/45\\x=224/45\end{array} \right.\)
Vậy x=-154/45 và x=224/45
b ta có (x-1/4)^2-25/64=0
(x-1/4)^2=25/64
(x-1/4)^2=(5/8)^2=(-5/8)^2
⇒ \(\left[ \begin{array}{l}x-1/4=5/8\\x-1/4=-5/8\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=7/8\\x=-3/8\end{array} \right.\)
Vậy x=5/8 hoặc x=-3/8
c ta có : (x-1/4)^2+17/64=21/32
(x-1/4)^2=21/32-17/64
(x-1/4)^2=42/64-17/64
(x-1/4)^2=25/64 (giải giống phần b )
d ta có 2/5.x+1/3=1/5
2/5.x=1/5-1/3
2/5.x=3/15-5/15
2/5.x=-2/15
⇒x=-2/15:2/5
x=-1/3
Vậy x=-1/3
e ta có 4/9-5/3.x=-2
5/3.x=4/9-(-2)
5/3.x=4/9+2
5/3.x=22/9
⇒x=22/15
vậy x=22/15
f ta có 5/7:x-3=-2/7
5/7:x=-2/7+3
5/7:x=19/7
⇒x=5/19
Vậy x=5/19
Bài $14$.
$a$) `8/2 – |7/9 – x| = -1/5`
`⇔ |7/9 – x | = 21/5`
`⇒` \(\left[ \begin{array}{l}x=\dfrac{-154}{45}\\x=\dfrac{224}{45}\end{array} \right.\)
Vậy $x$ $∈$ `{{-154}/{45};{224}/{45}}`
$b$) `(x-1/4)^2-{25}/{64}=0`
`⇔ (x-1/4)^2 = {25}/{64}`
`⇔ x-1/4 = ± 5/8`
`⇒` \(\left[ \begin{array}{l}x=\dfrac{7}{8}\\x=\dfrac{-3}{8}\end{array} \right.\)
Vậy $x$ $∈$ `{7/8;-3/8}`
$c$) `(x-1/4)^2+17/64=21/32`
`⇔ (x-1/4)^2 = {25}/64`
`⇔ x-1/4 = ± 5/8`
`⇒` \(\left[ \begin{array}{l}x=\dfrac{7}{8}\\x=\dfrac{-3}{8}\end{array} \right.\)
Vậy $x$ $∈$ `{7/8;-3/8}`
$d$) `2/5. x+1/3=1/5`
`⇔ 2/5 . x = -2/{15}`
`⇔ x = -1/3`
Vậy `x=-1/3`
$e$) ` 4/9-5/3 .x=-2`
`⇔ 5/3 . x = {22}/9`
`⇔ x = {22}/{15}`
Vậy `x = {22}/{15}`
$f$) `5/7 :x-3= -2/7`
`⇔ 5/7 😡 = {19}/7`
`⇔ x = 5/{19}`
Vậy `x = 5/{19}`
Bài $15$.
`A = 3/{1.3} + 3/{3.5} + 3/{5.7} + …. + 3/{199.201}`
`⇔ A/3 = 1/{1.3} + 1/{3.5} + 1/{5.7} + …. +1/{199.201}`
`⇔ A . 2/3 = 2/{1.3} + 2/{3.5} + 2/{5.7} + …. +2/{199.201}`
`⇔ A . 2/3 = 1/1 – 1/3 + 1/3 – 1/5 + 1/5 – 1/7 + ….. + 1/{199} – 1/{201}`
`⇔ A . 2/3 = {200}/{201}`
`⇔ A = {100}/{67}`
`B = 5/{1.3} + 5/{3.5} + 5/{5.7} + …. + 5/{201.203}`
`⇔ B/5 = 1/{1.3} + 1/{3.5} + 1/{5.7} + …. + 1/{201.203}`
`⇔ B . 2/5 = 2/{1.3} + 2/{3.5} + 2/{5.7} + …. +2/{201.203}`
`⇔ B . 2/5 = 1/1 – 1/3 + 1/3 – 1/5 + 1/5 – 1/7 + …. + 1/{201} – 1/{203}`
`⇔ B . 2/5 = {202}/{203}`
`⇔ B = {505}/{203}`