Réponse :
Bonsoir ;
Explications étape par étape
1)
(8x -1) (x+4) + (8x -1)(2x -3) = 0
(8x -1) ( x+4 +2x -3) = 0
(8x -1 ) ( 3x +1) =0
x= 1/8 ; x = -1/3
2)
(x-5) (2x -4) = 20
2x² -10x -4x +20-20 = 0
2x² -14x =0
2x ( x -7)
x =0 ; x = 7
3)
(5x -2)² = ( 3x -2) ( 6-15x )
(5x -2) (5x -2 +9x -6 ) =0
(5x -2 ) (14x -8) = 0
2( 5x -2 ) ( 7x -4 ) =0
x = 2/5 ; x = 4/7
4 )
(4x -3)² -9(x+1)² +2x² -12 x = 0
16x² +9 -24x -9(x² +2x +1) +2x² -12x =0
9x² -54x = 0
9x ( x -6) = 0
x = 0 ; x = 6
5)
(x²-x ) = 4x² -4
x(x-1) = 4(x²- 1)
x(x-1 )- 4( x²-1) = 0
( x -1) ((x-4(x+1)) =0
(x-1) ( x -4x -4 ) = 0
(x-1) ( -3x -4 ) =0
x =1 ; x = 4/3
6)
+2x² -2x[tex]\sqrt{6}[/tex] +3 = 8x² -12
+2x² -2x[tex]\sqrt{6}[/tex] +3 = 4( 2x² -3)
+2x² -2x[tex]\sqrt{6}[/tex] +3 = 4 ( x[tex]\sqrt{2}[/tex] - [tex]\sqrt{3}[/tex] ) ( x[tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex] )
+2x² -2x[tex]\sqrt{6}[/tex] +3 - 4 ( x[tex]\sqrt{2}[/tex] - [tex]\sqrt{3}[/tex] ) ( x[tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex] ) = 0
+2x² -2x[tex]\sqrt{6}[/tex] +3 = ( x[tex]\sqrt{2}[/tex] - [tex]\sqrt{3}[/tex] ) ( x[tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex] )
( x[tex]\sqrt{2}[/tex] - [tex]\sqrt{3}[/tex] ) ( x[tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex] ) - 4 ( x[tex]\sqrt{2}[/tex] - [tex]\sqrt{3}[/tex] ) ( x[tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex] ) = 0
( x[tex]\sqrt{2}[/tex] - [tex]\sqrt{3}[/tex] ) ( x[tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex] -4( x[tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex] ) ) = 0
( x[tex]\sqrt{2}[/tex] - [tex]\sqrt{3}[/tex] )( x[tex]\sqrt{2}[/tex] + [tex]\sqrt{3}[/tex] -4 x[tex]\sqrt{2}[/tex] -4 [tex]\sqrt{3}[/tex] ) = 0
( x[tex]\sqrt{2}[/tex] - [tex]\sqrt{3}[/tex] )( -3 [tex]\sqrt{3}[/tex] -3 x[tex]\sqrt{2}[/tex] ) = 0
-3( x[tex]\sqrt{2}[/tex] - [tex]\sqrt{3}[/tex] )( [tex]\sqrt{3}[/tex] + x[tex]\sqrt{2}[/tex] ) = 0
x = [tex]\sqrt{3}[/tex] /[tex]\sqrt{2}[/tex] ; x = - [tex]\sqrt{3}[/tex] /[tex]\sqrt{2}[/tex]
