4x^2 +y^2 -4x+10y+26=0 

4x^2-4x+1 +y^2+10y+25 =0

(2x-1)^2+(y+5)^2=0 

suy ra 2x-1=0 và y+5=0 

 x=1/2,y=-5

4x² + y² - 4x + 10y + 26 = 0

<=> ( 4x² - 4x + 1 ) + ( y² + 10y + 25 ) = 0

<=> ( 2x - 1 )² + ( y + 5 )² = 0

<=> \(\hept{\begin{cases}2x-1=0\\y+5=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\y=-5\end{cases}}\)

câu này căng đấy nhưng tớ sẽ cố giúp

thế này: 

4x² +y²-4x+10y+26=0.

= 4x\(^2\)- 4x+1+y\(^2\)+10x+25=0

= (2x-1)\(^2\)+ (y+5)\(^2\)= 0

=2x-1=0 và y+5=0

= x= 1/2 và y=-5

          \(4x^2+y^2-4x+10y+26=0\)

\(\Leftrightarrow\)\(\left(4x^2-4x+1\right)+\left(y^2+10y+25\right)=0\)

\(\Leftrightarrow\)\(\left(2x-1\right)^2+\left(y+5\right)^2=0\)

\(\Leftrightarrow\)\(\hept{\begin{cases}2x-1=0\\y+5=0\end{cases}}\)

\(\Leftrightarrow\)\(\hept{\begin{cases}x=\frac{1}{2}\\y=-5\end{cases}}\)

Vậy..

4x² - 4x + y² + 10y + 26 = 0

<=> [(2x)² - 2.2x + 1] + (y² + 2.5y + 5²) = 0

<=> (2x - 1)² + (y + 5)² = 0

Mà \(\left(2x-1\right)^2\ge0\forall x;\left(y+5\right)^2\ge0\forall y\)

nên \(\left\{{}\begin{matrix}\left(2x-1\right)^2=0\\\left(y+5\right)^2=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\y=-5\end{matrix}\right.\)

\(4x^2-4x+y^2+10y+26=0\)

=> \(4x^2-4x+y^2+10y+25+1=0\)

=> \(\left(4x^2-4x+1\right)+\left(y^2+10y+25\right)=0\)

=> \(\left(2x-1\right)^2+\left(y+5\right)^2=0\)

Ta thấy:

\(\left(2x-1\right)^2\ge0\)

\(\left(y+5\right)^2\ge0\)

=>\(\left(2x-1\right)^2+\left(y+5\right)^2\ge0\)

Mà \(\left(2x-1\right)^2+\left(y+5\right)^2=0\)

=>\(\left\{{}\begin{matrix}2x-1=0\\y+5=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x=\dfrac{1}{2}\\y=-5\end{matrix}\right.\)

Vậy x = \(\dfrac{1}{2}\); y = -5

\(4x^2+y^2-12x+10y+34=0\)

\(\Leftrightarrow4x^2-12x+9+y^2+10y+25=0\)

\(\Leftrightarrow\left(2x-3\right)^2+\left(y+5\right)^2=0\left(1\right)\)

mà \(\left\{{}\begin{matrix}\left(2x-3\right)^2\ge0,\forall x\\\left(y+5\right)^2\ge0,\forall y\end{matrix}\right.\)

\(\left(1\right)\Leftrightarrow\left\{{}\begin{matrix}\left(2x-3\right)^2=0\\\left(y+5\right)^2=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x-3=0\\y+5=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=-5\end{matrix}\right.\)

Ta có : \(4x^2+y^2-12x+10y+34=0\)

\(\Leftrightarrow4x^2-12x+9+y^2+10y+25=0\)

\(\Leftrightarrow\left(2x-3\right)^2+\left(y+5\right)^2=0\left(1\right)\)

Ta thấy : \(\left(2x-3\right)^2;\left(y+5\right)^2\ge0\)

Nên để (1) thoả mãn : 

\(\Leftrightarrow\left\{{}\begin{matrix}2x-3=0\\y+5=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=-5\end{matrix}\right.\)

Vậy........

4\(x^2\) + y² - 12\(x\) + 10y + 34 = 0

(4\(x^2\) - 12\(x\) + 9) + (y² + 10y + 25) = 0

(2\(x\) - 3)² + (y + 5)² = 0

(2\(x\) - 3)² ≥ 0 ∀ \(x\); (y + 5)² ≥ 0 ∀ y

(2\(x-3\))² + (y + 5)² = 0 ⇔ \(\left\{{}\begin{matrix}2x-3=0\\y+5=0\end{matrix}\right.\) ⇔ \(\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=-5\end{matrix}\right.\)

Kl: (\(x;y\)) = ( \(\dfrac{3}{2}\); -5)

\(\Leftrightarrow4x^2-12x+9+y^2+10y+25=0\)

\(\Leftrightarrow\left(2x-3\right)^2+\left(y+5\right)^2=0\) (1)

Do \(\left(2x-3\right)^2\ge0\) và \(\left(y+5\right)^2\ge0\)

\(\Rightarrow\left(1\right)\Leftrightarrow\left\{{}\begin{matrix}\left(2x-3\right)=0\\y+5=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=-5\end{matrix}\right.\)

Bài 1 : 

a, \(\left(x-3\right)^2-4=0\Leftrightarrow\left(x-3\right)^2=4\Leftrightarrow\left(x-3\right)^2=\left(\pm2\right)^2\)

TH1 : \(x-3=2\Leftrightarrow x=5\)

TH2 : \(x-3=-2\Leftrightarrow x=1\)

b, \(x^2-2x=24\Leftrightarrow x^2-2x-24=0\)

\(\Leftrightarrow\left(x-6\right)\left(x+4\right)=0\)

TH1 : \(x-6=0\Leftrightarrow x=6\)

TH2 : \(x+4=0\Leftrightarrow x=-4\)

c, \(\left(2x-1\right)^2+\left(x+3\right)^2-5\left(x+2\right)\left(x-2\right)=0\)

\(\Leftrightarrow4x^2-4x+1+x^2+6x+9-5\left(x^2-4\right)=0\)

\(\Leftrightarrow2x+30=0\Leftrightarrow x=-15\)

d, tương tự 

Bài 2 :

 \(x^2+2xy+y^2-6x-6y-5=\left(x+y\right)^2-6\left(x+y\right)-5\)

Thay x + y = -9 ta có : 

\(\left(-9\right)^2-6\left(-9\right)-5=130\)

Bài 1.

a) ( x - 3 )² - 4 = 0

<=> ( x - 3 )² - 2² = 0

<=> ( x - 3 - 2 )( x - 3 + 2 ) = 0

<=> ( x - 5 )( x - 1 ) = 0

<=> \(\orbr{\begin{cases}x-5=0\\x-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=5\\x=1\end{cases}}\)

b) x² - 2x = 24

<=> x² - 2x - 24 = 0

<=> x² + 4x - 6x - 24 = 0

<=> x( x + 4 ) - 6( x + 4 ) = 0

<=> ( x + 4 )( x - 6 ) = 0

<=> \(\orbr{\begin{cases}x+4=0\\x-6=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-4\\x=6\end{cases}}\)

c) ( 2x - 1 )² + ( x + 3 )² - 5( x + 2 )( x - 2 ) = 0

<=> 4x² - 4x + 1 + x² + 6x + 9 - 5( x² - 4 ) = 0

<=> 5x² + 2x + 10 - 5x² + 20 = 0

<=> 2x + 30 = 0

<=> 2x = -30

<=> x = -15

Bài 2.

D = x² + 2xy + y² - 6x - 6y - 5

= [ ( x² + 2xy + y² ) - 2x - 2y + 1 ] - 4x - 4y - 6

= [ ( x + y )² - 2( x + y ) + 1 ] - 4( x + y ) - 6

= ( x + y - 1 )² - 4( x + y ) - 6

Với x + y = -9

D = ( -9 - 1 )² - 4.(-9) - 6

    = 100 + 36 - 6

    = 130

Bài 3.

4x² + y² - 4x + 10y + 26 = 0

<=> ( 4x² - 4x + 1 ) + ( y² + 10y + 25 ) = 0

<=> ( 2x - 1 )² + ( y + 5 )² = 0

<=> \(\hept{\begin{cases}2x-1=0\\y+5=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\frac{1}{2}\\y=-5\end{cases}}\)