Verified answer

Bonsoir,

A)

9x-4=2x+5  <=>  9x-2x=5+4

                   <=>  7x=9

                   <=>  x=9/7

S={ 9/7 }

B)

x/4+2=0  <=>  x/4=-2

               <=>  x=-2*4

               <=>  x=-8

S={ -8 }

C)

3x-7=√2  <=>  3x=√2+7

               <=>  x=(√2+7)/3

S={ (√2+7)/3 }

D)

∀x∈R-{1/2}

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

                                <=>  2-3x=(3/2)*4x-2

                                <=>  2-3x=6x-3

                                <=>  2+3=6x+3x

                                <=>  5=9x

                                <=>  x=5/9

S={ 5/9 }

E)

(x+2)(2x+1)/3(x-2)²=0  <=>  (x+2)=0  ou  (2x+1)/3=0  ou  (x-2)²=0

                                    <=>  x=-2       ou  2x+1=0        ou  (x-2)=0

                                    <=>  x=-2       ou  x=-1/2          ou  x=2

S={ -2 ; -1/2 ; 2 }

F)

x²-10x+25=0  <=>  (x-5)²=0

                      <=>  x-5=0

                      <=>  x=5

S={ 5 }

G)

∀x∈R-{-1;2}

(2x-3)/(x+1)=(2x-3)/(2-x)  <=>  1/(x+1)=1/(2-x)   ou  2x-3=0

                                         <=>  1=(x+1)/(2-x)     ou  2x=3

                                         <=>  2-x=x+1             ou  x=3/2

                                         <=>  2-1=x+x

                                         <=>  1=2x

                                         <=>  x=1/2

S={ 1/2 ; 3/2 }

Exercice n°55 :

Il suffit de traduire l'énoncé sous forme d'équation, sachant que l'air d'un carré est égal au carré de son côté.

On a donc :

(x+3)²=x²+21  <=>  x²+6x+9=x²+21

                       <=>  x²-x²+6x=21-9

                       <=>  6x=12

                       <=>  x=12/6

                       <=>  x=2

La longueur initiale du carré est donc de 2cm.