Đáp án:

G. `x=2`

H. `x=1`

I. `x=\pm2`

Giải thích các bước giải:

G. `(4x-1)+2(4x-1)+3(4x-1)+\cdots+100(4x-1)=7+14+21+\cdots+700`

`=(4x-1)(1+2+3+\cdots+100)`

`=7(1+2+3+\cdots+100)`

`\Rightarrow (4x-1)(1+2+\cdots+100)=7(1+2+\cdots+100)`

`\Rightarrow 4x-1=7`

`\Rightarrow 4x=8`

`\Rightarrow x=2`

H. `(5x+1)+2(5x+1)+\cdots+101(5x+1)=6+12+18+\cdots+606`

`=(5x+1)(1+2+\cdots+101)`

`=6(1+2+\cdots+101)`

`\Rightarrow (5x+1)(1+2+\cdots+101)=6(1+2+\cdots+101)`

`\Rightarrow 5x+1=6`

`\Rightarrow 5x=5`

`\Rightarrow x=1`

I. `(x^2+1)+2(x^2+1)+\cdots+200(x^2+1)=5+10+15+\cdots+1000`

`=(x^2+1)(1+2+\cdots+200)`

`=5(1+2+\cdots+200)`

`\Rightarrow (x^2+1)(1+2+\cdots+200)=5(1+2+\cdots+200)`

`\Rightarrow x^2+1=5`

`\Rightarrow x^2=4`

`\Rightarrow x=\pm2`