Question

Sa se rezolve ecuatia : subpunctul f)

Answer 1

Răspuns:

folosesti formula arccosx=π/2-arcsin   x  

Ecuatia    devine

arcsinx[π-(π/2-arcsinx)]=π²/9

arcsinx(π/2+arcsinx)=π²/9

arcsinx=y    y∈[-1,1]

y(y+π/2)=π²/9

y²+πy/2-π²/9=0

Δ=π²/4+4π²/9=(9π²+16π²)/36=25π²/36

√Δ=√25π²/36=5π/6

y1=(-π/2-5π/6)*1/2=(-3π/6-5π/6)*1/2= -8π/12= -2π/3< -1   nu   convine  problemei

y2=(-π/2+5π/6)*1/2=(-3π+5π)/6*1/2=2π/6*1/2=π/6

arcsinx=π/6

x=1/2

Explicație pas cu pas: