résoudre l'inequation 100x+(140x)>(140-x)(100-x)

Bonjour

Résoudre l'inéquation :

100x+(140x)>(140-x)(100-x)

100x + 140x > 14000 - 140x - 100x + x^2

x^2 - 240x - 240x + 14000 < 0

x^2 - 480x + 14000 < 0

[tex]\Delta = (-480)^{2} - 4 \times 1 \times 14000 = 230400 - 56000 = 174400[/tex]

[tex]\sqrt\Delta \approx 417,6[/tex]

X1 = (480 - 417,6)/2 = 62,4/2 = 31,2

X2 = (480 + 417,6)/2 = 448,8

(X - 31,2)(x - 448,8) < 0

X..............|-inf..........(31,2)............(448,8).....+inf

x-31,2......|.........(-).......o........(+).................(+)......

x-448,8..|.........(-)...................(-).........o......(+).......

Ineq.......|..........(+)........||.........(-).........||.......(+).......

x € ]31,2 ; 448,8 [