`x^2-7x+2=0`

Theo Viet ta có `:`

`@x_1+x_2=7`

`@x_1x_2=2`

`A=(x_1)/(x_2)+((x_1+x_2).x_2)/(7x_2)`

`=(x_1)/(x_2)+(x_1+x_2)/7`

`=(x_1)/(x_2)+7/7`

`=(x_1)/(x_2)+1`

Đặt `t=(x_1)/(x_2)`

`=>A=t+1`

Mà `x_1=tx_2`

Mà `x_1x_2=2`

`=>tx_2^2=2`

Mà `x_1+x_2=7`

`=>tx_2+x_2=7`

`=>x_2(t+1)=7`

`=>x_2=7/(t+1)`

`=>t(7/(t+1))^2=2`

`=>(49t)/(t+1)^2=2`

`=>49=2(t+1)^2`

Đặt `u=t+1`

`=>49(u-1)=2u^2`

`=>49u-49=2u^2`

`=>2u^2-49u+49=0`

`=>(2u-49)(u-1)=0`

`=>u=49/2` hoặc `u=1`

`=>A=t+1=u=49/2`