PT có 2 nghiệm
`<=>Delta'>=0`
`<=>m^2-(m^2-m)>=0`
`<=>m>=0`
Áp dụng vi-ét ta có:
`x_1+x_2=2m,x_1.x_2=m^2-m`
`sqrtx_1/sqrtx_2+sqrtx_2/sqrtx_1=4`
`đk:x_1,x_2>0`
`=>x_1+x_2>0,x_1.x_2>0`
`=>m>1`
`pt<=>x_1/(sqrt{x_1.x_2})+x_2/(sqrt{x_1.x_2})=4`
`<=>(x_1+x_2)/(sqrt{x_1.x_2})=4`
`=>2m=4sqrt{m^2-m}`
`<=>m=2sqrt{m^2-m}`
`<=>m^2=4m^2-4m`
`<=>3m^2-4m=0`
`<=>m(3m-4)=0`
`<=>3m-4=0`(do `m>1`)
`<=>m=4/3(tm)`
Vậy `m=4/3` thì `sqrtx_1/sqrtx_2+sqrtx_2/sqrtx_1=4`.