Question

Rezolvati ecuatia: X supra lui X²- 4 = 2 supra X² +2x - 7 supra 2x-X²

Answer 1

x/(x²-4)=2/(x²+2x)-7/(2x-x²)
x/(x²-4)=2/(x²+2x)+7/(x²-2x)
x/(x²-4)=2(x²-2x)+7(x²+2x)/(x²+2x)(x²-2x)
x/(x²-4)=2x²-4x+7x²+14x)/(x⁴-4x²)
x/(x²-4)=(9x²+10x)/x²(x²-4)
x=(9x²+10x)/x²
x=(9x+10)/x
x²-9x-10=0
Δ=81+40=121
x₁=(9+√121)/2=(9+11)/2=10
x₂=(9-√121)/2=(9-11)/2=-1
x₁=10
x₂=-1