Question

[Bùi Khánh Chi]

Cho 3x + y = 3

a) Tìm min M = 3x2 + y2

b) Tìm max N = 2xy

Answer 1

[Nguyên Trần]

Có: 3x + y = 3 => y = 3x - 3

a) M = 3x² + y² = 3x² + ( 3x - 3)² = 3x² + 9x² - 18x + 9 = 3(4x² - 6x + 3) = 3(4x² - 6x +9/4) + 9/4 = 3(2x - 3/2)² + 9/4 \(\ge\)9/4

Vậy min M là 9/4

b) N = 2xy = 2x(3x - 3) = 6x² - 6x = 6(x² - x + 1/4 - 1/4) = 6(x - 1/2)² - 3/2 \(\le\)-3/2

Vậy max N là -3/2

Answer 2

[Đỗ Nguyễn Phương Thùy]

cảm ơn