Giải Bất Phương Trình Hai Ẩn Hay

By Trang Ánh Nam -

giải bất pt sau :cănxy+căn 1-x<=cănx ; x^2+y^2-x-y=2

Giải:

Bất phương trình xác định khi:

ð 0≤x≤1 ; y≥0.

Ta có:

   (*)

Điều kiện xác định: 0

=>

=>1-x≤x

=>   (1)

=>

=>

=>

=>  (2)

Từ (1) và (2) suy ra:     (I)

(*)<=>

ó

Điều kiện có nghiệm là: 1-xy≥0

=>1≥xy  (II)

Từ (I) và (II) suy ra 1≥xy≥1

=>x.y=1 và dấu bằng xãy ra khi x=1/2 và y=2

nhưng nghiệm :  không thỏa phương trình đã cho, nện hệ này vô nghiệm.

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