(x - 7)(x^2-9x+20)(x-2)=72
<=> [(x - 7)(x-2)](x^2 -9x + 20) = 72
<=> (x^2 -9x+14)(x^2-9x+20)=72
<=> (x^2 - 9x + 17 - 3)( x^2 - 9x +17 +3 ) = 72
<=> (x^2 - 9x +17 )^2 -3^2 = 72
<=> (x^2 - 9x + 17)^2 - 9 = 72
<=>( x^2 - 9x +17)^2 - 81 = 0
<=> (x^2 - 9x + 17)^2 - 9^2 = 0
<=> (x^2 - 9x + 17 - 9 )( x^2 -9x + 17 + 9 ) = 0
<=> (x^2 - 9x +8 )( x^2 -9x +26) = 0
<=> (x^2 - x - 8x + 8)[ (x^2 - 2.x.$\frac{9}{2}$ + $(\frac{9}{2})^{2}$) - $(\frac{9}{2})^{2}$ +26 ] = 0
<=> [x( x - 1 ) - 8( x - 1 ) ][ (x - $\frac{9}{2}$)^2 + $\frac{23}{4}$ ] = 0
<=> (x -1)( x-8)[ (x - $\frac{9}{2}$)^2 + $\frac{23}{4}$ ] =0
<=> \(\left[ \begin{array}{l}x-1=0\\x-8=0\\ [ (x - \frac{9}{2})^2 + \frac{23}{4} ] = 0 (vô \, \, lí \, \, nó \, \, luôn \, \, \geq \frac{23}{4} \, \, \forall x)\end{array} \right.\)
<=> \(\left[ \begin{array}{l}x=1\\x=8\end{array} \right.\)
x^2-2xy+6y^2-12x+2y+41 = 0
Vì: 6y^2 = 5y^2 + y^2
2y = 12y - 10y
41 = 36 + 5
Nên pt <=> x^2 - 2xy + y^2 + 5y^2 - 12x + 12y - 10y + 36 + 5 = 0
Nhóm các hạng tử với nhau: x^2 - 2xy + y^2 -12x + 12y + 36 + 5y^2 - 10y + 5 = 0
<=> ( x^2 - 2xy + y^2) - (12x - 12y) + 36 + (5y^2 - 10y + 5 ) = 0
<=> (x - y)^2 - 12( x - y) + 6^2 + 5( y^2 - 2y + 1 ) = 0
<=> ( x - y)^2 - 2.(x-y).6 + 6^2 + 5(y - 1)^2 = 0
<=> ( x - y - 6)^2 + 5( y - 1 )^2 = 0
<=> (x - y - 6)^2 + 5( y - 1)^2 = 0
<=> $\left \{ {{x- y - 6 = 0} \atop {y - 1 = 0}} \right.$
<=> $\left \{ {{x- y - 6 = 0} \atop {y =1}} \right.$
<=> $\left \{ {{x-1-6 = 0} \atop {y=1}} \right.$
<=> $\left \{ {{x-7=0} \atop {y=1}} \right.$
<=> $\left \{ {{x=7} \atop {y=1}} \right.$
