Question

Determina valorile lui p, p∈$R$, pentru care $p*|x-1|=|x|$ are cel putin o solutie reala

Answer 1

Explicație pas cu pas:

p*|x-1|=|x|

x<0

p(1-x)=-x

p-px=-x

x(p-1)=p

x=p/(p-1)

p/(p-1) <0

=>p€(0,1]

x€(0,1)

p(1-x)=x

p-px=x

x(p+1)=p

x=p/(p+1)

p/(p+1)=<1

p/(p+1)>0

=>p apartine unei multimi vide.

x€(1,+inf)

p(x-1)=x

px-p=x

x(p-1)=p

x=p/(p-1) >1=>p€(1,+inf)

Deci ecuatia are cel putin o solutie pt p€(1,+inf)

Bafta!