tìm x biết lx+1/2l+lx+1/6l+lx+1/12l+….+lx+1/110l=11x

0 bình luận về “tìm x biết lx+1/2l+lx+1/6l+lx+1/12l+….+lx+1/110l=11x”

1. `|x+1/2|+|x+1/6|+…+|x+1/110|=11x`

   VÌ `|x+1/2|≥0 ; |x+1/6|≥0 ;…;|x+1/110|≥0`

   Nên `|x+1/2|+|x+1/6|+…+|x+1/110|≥0`

   Suy ra `11x≥0`

       `⇒x≥0`

   Ta có:  `x+1/2+x+1/6+…+x+1/110=11x`

       `⇒10x+(1/(1×2)+1/(2×3)+…+1/(10×11)=11x`

       `⇒10x+(1-1/2+1/2-1/3+…+1/10-1/11)=11x`

       `⇒10x+(1-1/11)=11x`

       `⇒x=10/11`

    

   Bình luận

2. Đáp án:

   `|x+1/2|+|x+1/6|+|x+1/12|+….+|x+1/110|=11x`       `(1)`

   Vì `VT>=0 ∀x`

   `=> VP>=0 ∀x`

   `=> 11x>=0 ∀x`

   `=> x >=0 ∀x`

   `=> x+1/2>0 ∀x, x+1/6 >0 ∀x, x+1/12 >0 ∀x, …. , x+1/(110) >0 ∀x`

   `(1)` `=> x+1/2+x+1/6+….+x+1/110=11x`

   `=> (x+x+…+x)+(1/2+1/6+…+1/110)=11x`

   `=> (x+x+…+x)+(1/(1.2)+1/(2.3)+…+1/(10.11))=11x`

   `=> 10x+(1/1-1/11)=11x`

   `=> 10x+10/11=11x`

   `=> 10/11=11x-10x`

   `=> 10/11=x`

   Vậy `x=10/11`

   < Bài này cô đã chữa, bạn yên tâm tham khảo ^-^ >

    

   Bình luận