viết các biểu thức sau dưới dạng tổng của hai bình phương
1) a^2 -4ab+5b^2-4bc+4c^2
2)5x^2+y^2 +z^2+4xy-2xz
3)9x^2+25-12xy+2y^2-10y
4)13x^2 +4x-12xy+4y^2+1
5)x^2+4y^2+4x-4y+5
6)4x^2-12x+y^2-4y+13
7)x^2 +y^2+2y-6x+10
8)4x^2+9y^2-4x+6y+2
9)y^2+2y+5-12x+9x^2
10)x^2+26+6y+9y^2-10x
MN GIÚP MIK VS AK
Giải thích các bước giải:
Bạn kiểm tra lại đề bài câu 3
$\begin{array}{l}
1){a^2} – 4ab + 5{b^2} – 4bc + 4{c^2}\\
= \left( {{a^2} – 4ab + 4{b^2}} \right) + \left( {{b^2} – 4bc + 4{c^2}} \right)\\
= {\left( {a – 2b} \right)^2} + {\left( {b – 2c} \right)^2}\\
2)5{x^2} + {y^2} + {z^2} + 4xy – 2xz\\
= \left( {4{x^2} + 4xy + {y^2}} \right) + \left( {{x^2} – 2xz + {z^2}} \right)\\
= {\left( {2x + y} \right)^2} + {\left( {x – z} \right)^2}\\
3)9{x^2} + 25 – 6xy + 2{y^2} – 10y\\
= \left( {9{x^2} – 6xy + {y^2}} \right) + \left( {{y^2} – 10y + 25} \right)\\
= {\left( {3x – y} \right)^2} + {\left( {y – 5} \right)^2}\\
4)13{x^2} + 4x – 12xy + 4{y^2} + 1\\
= \left( {9{x^2} – 12xy + 4{y^2}} \right) + \left( {4{x^2} + 4x + 1} \right)\\
= {\left( {3x – 2y} \right)^2} + {\left( {2x + 1} \right)^2}\\
5){x^2} + 4{y^2} + 4x – 4y + 5\\
= \left( {{x^2} + 4x + 4} \right) + \left( {4{y^2} – 4y + 1} \right)\\
= {\left( {x + 2} \right)^2} + {\left( {2y – 1} \right)^2}\\
6)4{x^2} – 12x + {y^2} – 4y + 13\\
= \left( {4{x^2} – 12x + 9} \right) + \left( {{y^2} – 4y + 4} \right)\\
= {\left( {2y – 3} \right)^2} + {\left( {y – 2} \right)^2}\\
7){x^2} + {y^2} + 2y – 6x + 10\\
= \left( {{x^2} – 6x + 9} \right) + \left( {{y^2} + 2y + 1} \right)\\
= {\left( {x – 3} \right)^2} + {\left( {y + 1} \right)^2}\\
8)4{x^2} + 9{y^2} – 4x + 6y + 2\\
= \left( {4{x^2} – 4x + 1} \right) + \left( {9{y^2} + 6y + 1} \right)\\
= {\left( {2x – 1} \right)^2} + {\left( {3y + 1} \right)^2}\\
9){y^2} + 2y + 5 – 12x + 9{x^2}\\
= \left( {9{x^2} – 12x + 4} \right) + \left( {{y^2} + 2y + 1} \right)\\
= {\left( {3x – 2} \right)^2} + {\left( {y + 1} \right)^2}\\
10){x^2} + 26 + 6y + 9{y^2} – 10x\\
= \left( {{x^2} – 10x + 25} \right) + \left( {9{y^2} + 6y + 1} \right)\\
= {\left( {x – 5} \right)^2} + {\left( {3y + 1} \right)^2}
\end{array}$
`1) =(a^2-4ab+4b^2)+(b^2-4bc+4c^2)`
`=(a-2b)^2+(b-2c)^2 `
`2) =(4x^2+4xy+y^2)+(x^2-2xz+z^2`
`=(2x+y)^2+(x-z)^2`
`3) =(9x^2-6xy+y^2)+(y^2-10y+25)`
`=(3x-2y)^2+(2x+1)^2`
`5)=(x^2+4x+4)+(4y^2-4y+1)`
`=(x+2)^2+(2x+1)^2`
`6) =(4x^2-12x+9)+(y^2-4y+4)`
`=(x-3)^2+(y+1)^2`
`8) =(4x^2-4x+1)+(9y^2+6y+1)`
`=(2x-1)^2+(3y+1)^2`
`9)=(9x^2-12x+4)+(y^2+2y+1)`
`=(3x-2)^2+(y+1)^2`
`10)=(x^2-10x+25)+(9y^2+6y+1)`
`=(x-5)^2+(3y+1)^2`