Question

Se considera ecuatia x la 2-x+m=0 cu solutiile x1 si x2.Sa se determine numarul m pentru care 1 supra x1+1 +1 supra x2+1=-3 supra 4 CLASA 9 ECUATII DE GRADU 2

Answer 1

x²-x+m=0
x₁=[1+√(1-4m)]/2
x₂=[1-√(1-4m)]/2
1/(x₁+1)+ 1/(x₂+1) =-3 
1/{[1+√(1-4m)]/2 +1} + 1/{[1-√(1-4m)]/2+1}=-3
1/{[1+√(1-4m)]+2}/2 + 1/{[1-√(1-4m)]+2)/2=-3
1/[3+√(1-4m)]/2 + 1/[3-√(1-4m)]/2=-3.
2/[3+√(1-4m)] + 2/[3-√(1-4m)]=-3
2[3-√(1-4m)]/[3+√(1-4m)][3-√(1-4m)] + 2[3+√(1-4m)]/[3-√(1-4m)][3+√(1-4m)]=-3
2[3-√(1-4m)]/(9-1+4m) + 2[3+√(1-4m)]/(9-1+4m)=-3
6-2√(1-4m) + 6 +2√(1-4m)/(8+4m)=-3
12/(8+4m)=-3
3/(2+m)=-3
2+m=-1
m=-3