violympic có bài này á, chưa gặp bao giờ

1. (x + 2) * (x - 10) = 13

=> x² - 10x + 2x - 20 - 13 = 0

=> x² - 8x - 33 = 0

=> x² - 11x + 3x - 33 = 0

=> x*(x - 11) + 3*(x - 11) = 0

=> (x + 3) * (x -11) = 0

=> x + 3 = 0 hoặc x - 11 = 0

=> x = -3 hoặc x = 11

2. Tìm GTBT 3x - 6y +70⁽¹⁾ tại 2y - x = -25

2y - x = -25

=> -(2y - x) = 25

=> -2y + x = 25 => x - 2y = 25^(*)

⁽¹⁾= 3*(x - 2y) + 70

Thay ^(*) vào ⁽¹⁾ 

⁽¹⁾= 3 * 25 + 70 = 145

\(2x^2+2y^2-2xy-6y+21\)

\(2A=4x^2+4y^2-4xy-12y+42\)

\(=4x^2-4xy+4y^2-12y+42\)

\(=4x^2-4xy+y^2+3y^2-12y+42\)

\(=\left(4x^2-4xy+y^2\right)+\left(3y^2-12y+42\right)\)

\(=\left(2x-y\right)^2+3\left(y^2-4x+4\right)+30\)

\(=\left(2x-y\right)^2+3\left(y-2\right)^2+30\ge30\)

Vậy GTNN là 30

Cho mk sủa lại tí :

\(2A=4x^2+4y^2-4xy-12y+42\)

\(=4x^2-4xy+4y^2-12+42\)

\(=4x^2-4xy+y^2+3y^2-12y+42\)

\(=\left(2x-y\right)^2+3\left(y-2\right)^2+30\ge30\)

\(\Rightarrow2A\ge30\Rightarrow A\ge15\Rightarrow\)GTNN là 15

\(2x^2+2y^2-4xy+2x-2y+4\)

\(=2\left(x-y\right)^2+2\left(x-y\right)+4\)

\(=2\left[\left(x-y\right)^2+2\left(x-y\right)\frac{1}{2}+\frac{1}{4}\right]+\frac{7}{2}\)

\(=2\left(x-y+\frac{1}{2}\right)^2+\frac{7}{2}\)

\(\Rightarrow A\ge\frac{7}{2}\)

Dấu = bn tự tính nhé