Tìm x, biết: 1/10 + 1/40 + 1/88 + … + 1/(3x+2)(3x+5) = 4/25 01/11/2021 Bởi Kennedy Tìm x, biết: 1/10 + 1/40 + 1/88 + … + 1/(3x+2)(3x+5) = 4/25
Đáp án: Giải thích các bước giải: $\dfrac{1}{10}+\dfrac{1}{40}+…+\dfrac{1}{(3x+2)(3x+5)}=\dfrac{4}{25}$ $ $ $⇒\dfrac{3}{2.5}+\dfrac{3}{5.8}+…+\dfrac{3}{(3x+2)(3x+5)}=\dfrac{12}{25}$ $ $ $⇒\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+…+\dfrac{1}{3x+2}-\dfrac{1}{3x+5}=\dfrac{12}{25}$ $ $ $⇒\dfrac{1}{2}-\dfrac{1}{3x+5}=\dfrac{12}{25}$ $ $ $⇒\dfrac{1}{3x+5}=\dfrac{1}{50}$ $ $ $⇒3x+5=50$ $⇒3x=45$ $⇒x=15$ Bình luận
Đáp án: `x=15` Giải thích các bước giải: `1/10 + 1/40 + 1/88 + … + 1/((3x+2)(3x+5)) = 4/25` `⇒1/2.5 + 1/5.8 + 1/8.11 + … + 1/((3x+2)(3x+5)) = 4/25` `⇒3/2.5 + 3/5.8 + 3/8.11 + … + 3/((3x+2)(3x+5)) = 12/25` (nhân 2 vế với 3) `⇒1/2-1/5 + 1/5-1/8 + 1/8-1/11 + … + 1/(3x+2)-1/(3x+5) = 12/25` `⇒1/2-1/(3x+5) = 12/25` `⇒1/(3x+5) = 1/2-12/25` `⇒1/(3x+5) = 1/2-12/25` `⇒1/(3x+5) = 1/50` `⇒3x+5=50` `⇒3x=45` `⇒x=15` Vậy `x=15`. Bình luận
Đáp án:
Giải thích các bước giải:
$\dfrac{1}{10}+\dfrac{1}{40}+…+\dfrac{1}{(3x+2)(3x+5)}=\dfrac{4}{25}$
$ $
$⇒\dfrac{3}{2.5}+\dfrac{3}{5.8}+…+\dfrac{3}{(3x+2)(3x+5)}=\dfrac{12}{25}$
$ $
$⇒\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+…+\dfrac{1}{3x+2}-\dfrac{1}{3x+5}=\dfrac{12}{25}$
$ $
$⇒\dfrac{1}{2}-\dfrac{1}{3x+5}=\dfrac{12}{25}$
$ $
$⇒\dfrac{1}{3x+5}=\dfrac{1}{50}$
$ $
$⇒3x+5=50$
$⇒3x=45$
$⇒x=15$
Đáp án:
`x=15`
Giải thích các bước giải:
`1/10 + 1/40 + 1/88 + … + 1/((3x+2)(3x+5)) = 4/25`
`⇒1/2.5 + 1/5.8 + 1/8.11 + … + 1/((3x+2)(3x+5)) = 4/25`
`⇒3/2.5 + 3/5.8 + 3/8.11 + … + 3/((3x+2)(3x+5)) = 12/25` (nhân 2 vế với 3)
`⇒1/2-1/5 + 1/5-1/8 + 1/8-1/11 + … + 1/(3x+2)-1/(3x+5) = 12/25`
`⇒1/2-1/(3x+5) = 12/25`
`⇒1/(3x+5) = 1/2-12/25`
`⇒1/(3x+5) = 1/2-12/25`
`⇒1/(3x+5) = 1/50`
`⇒3x+5=50`
`⇒3x=45`
`⇒x=15`
Vậy `x=15`.