.............................................................................

`5) 9x^2 + 4y^2 + 26 + 4y = 30x`

`\iff (9x^2 - 30x + 25) + (4y^2 + 4y + 1) = 0`

`\iff (3x-5)^2 + (2y + 1)^2 = 0(\star)`

Do `(3x-5)^2 \ge 0`;`(2y+1)^2\ge0`

`=> (3x-5)^2 + (2y + 1)^2 \ge 0`

`(\star) \iff {(3x-5=0),(2y+1=0):} \iff {(3x=5),(2y=-1):} \iff {(x=5/3),(y=-1/2):}`

Vậy `(x;y)=(5/3 ; -1/2)`

`6)` `9x^2 + y^2 + 20 = 12x + 8y`

`\iff (9x^2 - 12x + 4) + (y^2 - 8y + 16) = 0`

`\iff (3x-2)^2 + (y-4)^2 = 0`

`\iff {(3x - 2 = 0),(y-4=0):} \iff {(3x=2),(y =4):} \iff {(x = 2/3),(y=4):}`

Vậy `(x;y) = (2/3;4)`

`7)``x^2 + 49y^2 + 5 + 14y = 4x`

`\iff (x^2 - 4x + 4) + (49y^2 + 14y + 1) = 0` 

`\iff (x-2)^2 + (7y + 1)^2 = 0`

`\iff {(x-2=0),(7y+1=0):}`

`\iff {(x=2),(7y=-1):}`

`\iff {(x=2),(y=-1/7):}`

Vậy `(x;y) = (2;-1/7)`

`8)` `16x^2 + 25y^2 + 13 = 20y + 24x`

`\iff (16x^2 - 24x + 9) + (25y^2 - 20y + 4) = 0`

`\iff (4x - 3)^2 + (5y - 2)^2 = 0`

`\iff {(4x -3 = 0),(5y - 2 = 0):}`

`\iff {(4x =3),(5y =2):}`

`\iff {(x =3/4),(y =2/5):}`

Vậy `(x;y) = (3/4;2/5)`

Áp dụng : `a^2 + b^2 = 0 \iff {(a=0),(b=0):}`