Question

Se considera x^2-(2m-1)x+m+1=0, m ap R cu radacinile x1 si x2. Determinati m ap R stiind ca x1^2 * x2=x1* x2^2

Answer 1

Explicație pas cu pas:

x1^2*x2=x1*x2^2

x1^2/x1 = x2^2/x2

x1=x2=t

x1+x2=2m-1=>t=(2m-1)/2

x1*x2=m+1=>t^2=m+1

=>(2m-1)^2/4=m+1

sau:

Conditie: delta=0

delta=(2m-1)^2-4m-4=0

4m^2-4m+1-4m-4=0

4m^2-8m-3=0

delta=64+48=112

m1=2+radical(7)

m2=2-radical(7)

Bafta!