Réponse :
a) (5x-3)(x-5)= (2x+5)²+90
5x²-25x-3x+15 = 4x²+20x+25+90
5x²-28x+15=4x²+20x+115
5x²-28x+15-4x²-20x-115=0
x²-48x-100=0
b²-4ac = (-48)²-4(1*-100)=2704
Δ>0 2solutions
(-b-√Δ)/2a=(48-52)/2 =-2
(-b+√Δ)/2a = (48+52)/2=50
S{-2;50}
x+[tex]\frac{1}{x}[/tex]=2
x≠0
x+ 1/x - 2 =0
(x²+1-2x)/x=0
x²-2x+1=0
(x-1)²=0
x=1
3x+5/2x+1 = 4x+7/x-1
x≠-1/2;1
(3x+5)(x-1) = (4x+7)(2x+1)
(3x+5)(x-1) -(4x+7)(2x+1)=0
3x²-3x+5x-5-(8x²+4x+14x+7)=0
3x²+2x-5-8x²-18x-7=0
-5x²-16x-12=0
b²-4ac= (-16)²-4(-5*-12) =16
Δ>0 2solutions
(-b-√Δ)/2a =(16-4)/-10 =12/-10= -6/5
(-b+√Δ)/2a=(16+4)/-10 = -2
S{-6/5;-2}
3x²-27/2x²+6x=0
x≠-3;0
3(9x²-9)/2x(x+3)=0
3(3x-3)(3x+3)/2x(x+3)=0
3(x-3)/2x=0
x=3
x-5/x-1 + x-3/x-2 = -9x+17/(x-1)(x-2)
x≠1;2
x-5/x-1 + x-3/x-2 -(-9x+17/(x-1)(x-2))=0
[(x-5)(x-2)+(x-3)(x-1)+9x-17]/(x-1)(x-2)=0
(x²-5x-2x+10+x²-3x-x+3+9x-17)/(x-1)(x-2)=0
(2x²-2x-4)/(x-1)(x-2)=0
2x²-2x-4=0
b²-4ac=(-2)²-4(2*-4)=36
Δ>0 2solutions
(-b+√Δ)/2a =(2+6)/4 =2
(-b-√Δ)/2a=(2-6)/4 =-1
S{2;-1}
Explications étape par étape :
