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m∈R, (m-1)x²+2(1-m)x+1=0, Δ=0 aflati parametrul m.

Răspuns :

delta = [2(1-m)] la patrat -4(m-1) = 4(1-2m+m patrat)-4(m-1)=0. Imparti prin 4 =>
1-2m+m patrat -m+1=0 =>m patrat -3m+2=0 => delta = 1 => m1=(3+1)/2=2 si m2=(3-1)/2=1 nu convine => S={2}
(m-1)x²+2(1-m)x+1=0⇒
(m-1)+(2+2m)x+1=0⇒
a=m+1
b=2-2m
c=1
d=b²-4ac⇒D=(2-2m)²-4(m-1)×1=d=4-4m+4m²-4m+4
d=4m²⇔d=