Bonsoir,

Développer f(x)

f(x)= 25x²-(2x-3)²

f(x)= 25x²-(4x²-6x-6x+9)

f(x)= 25x²-4x²+12x-9

f(x)= 21x²+12x-9

Factoriser f(x)

f(x)= 25x²-(2x-3)²

f(x)= (5x)²-(2x-3)²

f(x)= (5x-2x+3)(5x+2x-3)

f(x)= (3x+3)(7x-3)

f(x)= 3(x+1)(7x-3)

Calcul de f(-4/7)

f(x)= 21x²+12x-9

f(-4/7)= 21(-4/7)²+12(-4/7)-9

f(-4/7)= 21(16/49)-(48x7)/49- (9x49)/49

f(-4/7)= 336/49-336/49- 441/49

f(-4/7)= -9

Résoudre f(x)= 0

3(x+1)(7x-3)= 0

x= -1 ou x= 3/7

S= { -1 ; 3/7 }

Résoudre (2-5x)/2 - (7x+3)/14 ≤ 1

7 (2-5x)/14 - (7x+3)/14 ≤ 14/14

14- 35x-7x-3 ≤ 14

-35x-7x ≤ 14-14+3

-42x ≤ 3

x ≥ -3/42

x ≥ -1/14

S= [ -1/14 ; +∞ [