Question

[gamoi123]

3xX/4+3xX/28+3xX/70+...+3xX/304=18/19

Answer 1

[Mike]

3x/4 + 3x/28 + 3x/70 +  ... + 3x/304 = 18/19

=> x(3/1*4 + 3/4*7 + 3/7*10 + ... + 3/16*19) = 18/19

=> x(1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/16 - 1/19) = 18/19

=> x(1 - 1/19) = 18/19

=> x*18/19 = 18/19

=> x = 1

Answer 2

[xKraken]

\(3.\frac{x}{4}+3.\frac{x}{28}+3.\frac{x}{70}+...+3.\frac{x}{304}=\frac{18}{19}\)

\(3.\left(\frac{x}{4}+\frac{x}{28}+\frac{x}{70}+...+\frac{x}{304}\right)\)

\(\frac{x}{4}+\frac{x}{28}+\frac{x}{70}+...+\frac{x}{304}=\frac{18}{19}:3=\frac{6}{19}\)

Nhân hai vế với 3/x ta được

\(\frac{3}{x}\left(\frac{x}{4}+\frac{x}{28}+\frac{x}{70}+...+\frac{x}{304}\right)=\frac{6}{19}.\frac{3}{x}\)

\(\frac{3}{x}.\frac{x}{4}+\frac{3}{x}.\frac{x}{28}+\frac{3}{x}.\frac{x}{70}+...+\frac{3}{x}.\frac{x}{304}=\frac{18}{19.x}\)

\(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+...+\frac{3}{304}=\frac{18}{19}:x\)

\(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{16.19}=\frac{18}{19}:x\)

\(1-\frac{1}{19}=\frac{18}{19}:x\)

\(\frac{18}{19}=\frac{18}{19}:x\)

\(x=\frac{18}{19}:\frac{18}{19}=1\)

Chúc bạn học tốt !!!

P/s: Không hiểu chỗ nào cứ ib