Tìm số tự nhiên x biết: a)1+3+5+7+9+…+(2x-1)=225 b) 2^x+2^x+1+2^x+2+2^x+3+…+2^x+2015+=2^2019-8 07/11/2021 Bởi Raelynn Tìm số tự nhiên x biết: a)1+3+5+7+9+…+(2x-1)=225 b) 2^x+2^x+1+2^x+2+2^x+3+…+2^x+2015+=2^2019-8
Đáp án: `↓↓` Giải thích các bước giải: `a) 1+3+5+…+(2x-1)=225` `=> (1+2x-1). (2x-1+1)/2 : 2=225` `=> 2x. x/2=225` `=> 2x^2=450` `=> x^2=225` `=> x=+-15` `b) 2^x+2^(x+1)+2^(x+2)+…+2^(x+2015)=2^(2019)-8` `=> 2^x+2^x. 2+2^x. 2^2+…+2^x. 2^(2015))=2^(2019)-8` `=> 2^x. (1+2+2^2+….+2^(2015))=2^(2019)-8` `=> 2^x . (2^(2016)-1)=2^(2019)-8` `=> 2^x=(2^(2019)-8)/(2^(2016)-1)` `=> 2^x=(2^3. (2^(2016)-1))/(2^(2016)-1)` `=> 2^x=2^3` `=> x=3` $\boxed{\text{Khánh Huyền}}$ Bình luận
a)1+3+5+7+9+…+(2x-1)=225 ⇒(1+2n-1).n:2=n² ⇒1+3+5+7+9+…+(2x-1)=n² ta có :225=3².5²=(3.5)²=15² vậy n=15 b) 2^x+2^x+1+2^x+2+2^x+3+…+2^x+2015+=2^2019-8 ⇔2^x.(1+2+2²+…+2^2015)=2^2019-2³ ⇔2^x.(2^2016-1)=2^3.(2^2016-1) ⇔2^x=2^3 vậy x=3 cho mk xin ctlhn nhé Bình luận
Đáp án:
`↓↓`
Giải thích các bước giải:
`a) 1+3+5+…+(2x-1)=225`
`=> (1+2x-1). (2x-1+1)/2 : 2=225`
`=> 2x. x/2=225`
`=> 2x^2=450`
`=> x^2=225`
`=> x=+-15`
`b) 2^x+2^(x+1)+2^(x+2)+…+2^(x+2015)=2^(2019)-8`
`=> 2^x+2^x. 2+2^x. 2^2+…+2^x. 2^(2015))=2^(2019)-8`
`=> 2^x. (1+2+2^2+….+2^(2015))=2^(2019)-8`
`=> 2^x . (2^(2016)-1)=2^(2019)-8`
`=> 2^x=(2^(2019)-8)/(2^(2016)-1)`
`=> 2^x=(2^3. (2^(2016)-1))/(2^(2016)-1)`
`=> 2^x=2^3`
`=> x=3`
$\boxed{\text{Khánh Huyền}}$
a)1+3+5+7+9+…+(2x-1)=225
⇒(1+2n-1).n:2=n²
⇒1+3+5+7+9+…+(2x-1)=n²
ta có :225=3².5²=(3.5)²=15²
vậy n=15
b) 2^x+2^x+1+2^x+2+2^x+3+…+2^x+2015+=2^2019-8
⇔2^x.(1+2+2²+…+2^2015)=2^2019-2³
⇔2^x.(2^2016-1)=2^3.(2^2016-1)
⇔2^x=2^3
vậy x=3
cho mk xin ctlhn nhé