Giai truong hop tong quat luon:Dieu kien: x≥2;y≥1. Tu PT (2) suy ra m≥0. He da cho tuong duong voi:
{√x+1+√x−2+√y+2+√y−1=2m+2√x+1−√x−2+√y+2−√y−1=2
Dat {a=√x+1+√x−2(a>0)b=√y+2+√y−1(b>0), ta co:
{√x+1−√x−2=3a√y+2−√y−1=3b,
Khi do he da cho tro thanh:
{a+b=2m+23a+3b=2
⇔{a+b=2m+2ab=3(m+1)
Theo dinh li Viete dao, he da cho co nghiem khi va chi khi:
S2≥4P⇔(2m+2)2≥4.3(m+1)⇔m≥2.
KL: he PT da cho co nghiem khi va chi khi m≥2.
Ap dung voi m=2, ta co:
{a+b=6ab=9⇔a=b=3 (vi a,b>0)
⇔{√x+1+√x−2=3√y+2+√y−1=3 (giai 2 PT nay bang PP lien hop hay binh phuong tuy em.)
⇔{x=3y=2.
Neu thay hay thi vote manh vao...:))