Question

[Nhi Hàn Băng]

Viết dưới dạng tổng hai bình phương

1) \(4x^2-12x+y^2-4y+13\)

2) \(x^2+y^2+2y-6x+10\)

3) \(4x^2+9y^2-4x+6y+2\)

4) \(y^2+2y+5-12x+9x^2\)

5) \(x^2+26+6y+9y^2-10x\)

Answer 1

[Nhã Doanh]

1) \(4x^2-12x+y^2-4y+13\)

\(=\left(4x^2-12x+9\right)+\left(y^2-4y+4\right)\)

\(=\left[\left(2x\right)^2-2.2x.3+3^2\right]+\left(y^2-2.2y+4\right)\)

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

2) \(x^2+y^2+2y-6x+10\)

\(=\left(x^2+2y+1\right)+\left(y^2-6x+9\right)\)

\(=\left(x+1\right)^2+\left(y-3\right)^2\)

3) \(4x^2+9y^2-4x+6y+2\)

\(=\left(4x^2-4x+1\right)+\left(9y^2+6y+1\right)\)

\(=\left(2x-1\right)^2+\left(3y+1\right)^2\)

4) \(y^2+2y+5-12x+9x^2\)

\(\left(y^2+2y+1\right)+\left(9x^2-12x+4\right)\)

\(=\left(y+1\right)^2+\left(3x-2\right)^2\)

5) \(x^2+26+6y+9y^2-10x\)

\(=\left(x^2-10x+25\right)+\left(9y^2+6y+1\right)\)

\(=\left(x-5\right)^2+\left(3y+1\right)^2\)