Je sais pas si vous allez comprendre mais ça vaut le coup on a: A=-20x²+36x-16 =-20[x²-(36/20)x+16/20] =-20[x²-(9/5)x+4/5] =-20[(x-(9/10))²-(81/100)+4/5] = -20[(x-(9/10))²-(81/100)+(80/100)] = -20[(x-(9/10))²-(1/100)] on pose A=0⇒ [(x-(9/10))²-(1/100)]=0 [(x-(9/10))²-(1/10)²]=0 [(x-(9/10)-(1/10))(x-(9/10)+(1/10))]=0 [x-(10/10)][x-(8/10)]=0 ⇒x-1=0 ou x-4/5=0
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Je sais pas si vous allez comprendre mais ça vaut le coupon a: A=-20x²+36x-16
=-20[x²-(36/20)x+16/20]
=-20[x²-(9/5)x+4/5]
=-20[(x-(9/10))²-(81/100)+4/5]
= -20[(x-(9/10))²-(81/100)+(80/100)]
= -20[(x-(9/10))²-(1/100)]
on pose A=0⇒ [(x-(9/10))²-(1/100)]=0
[(x-(9/10))²-(1/10)²]=0
[(x-(9/10)-(1/10))(x-(9/10)+(1/10))]=0
[x-(10/10)][x-(8/10)]=0
⇒x-1=0 ou x-4/5=0
x=1 ou x=4/5
S={1, 4/5}