Đáp án:
Thay `x=sqrt{2}` vào pt :
`(m-4)sqrt{2²}-msqrt{2}+m-2=0`
`⇔(m-4)2-msqrt{2}+m-2=0`
`⇔3m-msqrt{2}=10`
`⇔m(3-sqrt{2})=10`
`⇔m=frac{30+10sqrt{2}}{7}`
Áp dụng hệ thức Vi ét ta có :
`x_1+x_2=frac{-b}{a}=frac{frac{30+10sqrt{2}}{7}}{frac{2+10sqrt{2}}{7}`
`⇔sqrt{2}+x_2=frac{30+10sqrt{2}}{7}:frac{2+10sqrt{2}}{7}`
`⇔sqrt{2}+x_2=frac{(30+10sqrt{2})7}{(2+10sqrt{2})7}`
`⇔sqrt{2}+x_2=frac{30+10sqrt{2}}{2+10sqrt{2}}`
`⇔sqrt{2}+x_2=frac{5+10sqrt{2}}{7}`
`⇔x_2=frac{5+10sqrt{2}}{7}-sqrt{2}`
`⇔x_2=frac{5+3sqrt{2}}{7}`
Vậy `m=frac{30+10sqrt{2}}{7}` ; nghiệm còn lại `x_2=frac{5+3sqrt{2}}{7}`
$\text{Shield Knight}$
