Mathématiques

Question

Bonjour



Je voudrais savoir si mes résultats de ces équations sont bonnes (surtout pour la f et la g svp, merci) :



a) (x+3)² = (x+1)(x+3)



(x+3)[(x+3)-(x+1)]=0

(x+3)(x+3-x-1)=0

(x+3)(2)=0



s= -3



b) x²+5 = 0



x²= -5 (impossible)



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



s= (-1;5/2;-1/3)



d)25x²-10x+1 = (5x-1)(2x+3)



(5x-1)²-(5x-1)(2x+3)=0

(5x-1)[(5x-1)-(2x+3)]=0

(5x-1)(3x-4)=0



s= (1/5;4/3)



e)x^3+8x²+16x= 0



x(8x+16)=0



s= (0;-2)



f) 4/2-x = 3/5

Valeurs interdite : x=2



4-3(2-x)/2-x = 0



-2+3x/2-x = 0



-2+3x = 0



s = 2/3



g) x+5/x+1 = x-1/x-5

Valeurs interdites : -1 et 5



(x+5)(x-5)-(x+1)(x+1)/(x+1)(x-5) = 0

x²-25-x²-x+x+1/(x+1)(x-5) =0

26/(x+1)(x-5)

26=0 (impossible)

1 Réponse

  • Bonjour

    a) (x + 3)² = (x + 1)(x + 3)
    (x + 3)² - (x + 1)(x + 3) = 0
    (x + 3)[(x + 3) - (x + 1)]=0
    (x + 3)(x + 3 - x - 1)= 0
    2(x + 3) = 0
    x + 3 = 0
    x = -3 
    S = {-3}

    b) x² + 5 = 0
    x² = -5
    Equation impossible
    S = Ф

    c) (x +1 )(2x - 5)(3x + 1) = 0
    x + 1 = 0  ou  2x - 5 = 0  ou  3x + 1 = 0
    x = -1   ou  2x = 5   ou  3x = -1
    x = -1   ou  x = 5/2   ou  x = -1/3
    S = {-1 ; 5/2 ; -1/3}

    d) 25x² - 10x + 1 = (5x - 1)(2x + 3)
    (5x - 1)² = (5x - 1)(2x + 3)
    (5x - 1)² - (5x - 1)(2x + 3) = 0
    (5x - 1)[(5x - 1) - (2x + 3)] = 0
    (5x - 1)(5x - 1 - 2x - 3) = 
    (5x - 1)(3x - 4) = 0
    5x - 1 = 0   ou   3x - 4 = 0
    5x = 1   ou   3x = 4
    x = 1/5   ou  x = 4/3
    S = {1/5 ; 4/3}

    e) x^3 + 8x² + 16x = 0
    x(x² - 8x + 16) = 0
    x(x - 4)² = 0
    x = 0   ou  (x - 4)² = 0
    x = 0   ou   x - 4 = 0
    x = 0   ou   x = 4
    S = {0 ; 4}

    [tex]f)\ \dfrac{4}{2-x} = \dfrac{3}{5}\\\\Valeur\ interdite\ :\ x = 2\\\\4\times5=3\times(2-x)\\\\20=6 - 3x\\\\3x=6-20\\\\3x=-14\\\\x=\dfrac{-14}{3}\\\\S=\{\dfrac{-14}{3}\}[/tex]


    [tex]g)\ \dfrac{x+5}{x+1}=\dfrac{x-1}{x-5}\\\\Valeurs\ interdites\ :\ x=-1\ \ et\ \ x=5\\\\(x+5)(x-5)=(x+1)(x-1)\\\\x^2-25=x^2-1\\\\-25=-1\\\\Impossible\\\\S=\phi[/tex]



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