Câu hỏi của Nhi Hàn Băng

Question

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) $x^2+26+6y+9y^2-10x$

Nhã Doanh · Accepted Answer

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)   $x^2+26+6y+9y^2-10x$

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

$=\left(x-5\right)^2+\left(3y+1\right)^2$Câu trả lời: 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)   $x^2+26+6y+9y^2-10x$

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

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

Bài 4: Những hằng đẳng thức đáng nhớ (Tiếp)