Bonjour,
Résoudre les inéquations:
(3-2x)/(x+2) ≤ (-4x + 12)/ (2x+1)
[ (3-2x)/(x+2) - [ (-4x + 12) / (2x+1) ] ≤ 0
x ≠ -2, x≠ -1/2
[ (3-2x)(2x+1)- (-4x+12)(x+2)]/ [ (x+2)(2x+1) ] ≤ 0
[ 6x-4x²+3-2x-(-4x²+12x-8x+24) ] / [ (x+2)(2x+1) ] ≤ 0
[ 4x-4x²+3-(-4x²+4x+24) ] / [ (x+2)(2x+1) ] ≤ 0
(-4x²+4x+3+4x²-4x-24) / [ (x+2)(2x+1) ] ≤ 0
-21/ / [ (x+2)(2x+1) ] ≤ 0
S= ] - ∞ ; -2 [ U ] -1/2; +∞ [
[(6x-3)(x-4)-(2x-1)(5x-3)] / (x²+1-2x) < 0
[ 6x²-3x-24x+12-(10x²-11x+3) ] / (x²+1-2x) < 0
(6x²-27x+12-10x²+11x-3) / (x²+1-2x) < 0
(-4x²-16x+9) / (x²+1-2x) < 0 noter: a < 0
Δ= b²-4ac= (-16)²-4(-4)(9)= 400 > 0, 2 solutions.
x1= (-b-√Δ)/2a= ( -(-16)- √400)/2(-4)= (16-20)/-8= -4//-8= 1/2
x2= (-b+√Δ)/2a= ( -(-16)+ √400)/2(-4)= (16+20)/-8= -36/8= -9/2
S= ] - ∞ ; -9/2 [ U ] 1/2; 1 [ U ]1 ; +∞ [
Pour les inéquations, faire un tableau pour mieux comprendre, tenir comptes des valeurs interdites.
Résoudre l'équation:
(5x-3)/(x-3) = (6-10x)/ (x+1)
(5x-3)(x+1)= (6-10x)(x-3)
5x²-3x+5x-3= 6x-10x²-18+30x
5x²+2x-3= -10x²+36x-18
5x²+2x-3+10x²-36x+18= 0
15x²-34x+15= 0
Δ= (-34)²-4(15)(15)= 256 > 0
x1= (34-16)/30 = 18/30= 3/5
x2= (34+16)/30= 50/30= 5/3
S= { 3/5 ; 5/3 }
