Rozwiąż równania a) x-2 6x-1 3- --------- = ---------- x+2 5x-9 b) x5-x4-5x3-6x+6=0 c)5x4-6x3=0

a) x-2=6x-1 x-6x=2-1 -5x=1 |:-5 x=- jedna piąta b) x5-x4-5x3-6x+6=0 -20x=-6 |:-20 x=0,3 c)5x4-6x3=0 20x-18x=0 2x=0 |:2 x=0

Rozwiąż równania a) 3-x-2/x+2= 6x-1/5x-9|* (x+2)(5x-9) (x+2)(5x-9)*3-(x+2)(5x-9)*x-2/x+2=(x+2)(5x-9)*6x-1/5x-9 (5x²-9x+10x-18)*3-(5x-9)(x-2)=(x+3)(6x-1) (5x²+x-18)*3-(5x²-10x-9x+18)=6x²-x+18x-3 15x²+3x-54-5x²+19x-18=6x²+17x-3 4x²+5x-69=0 Δ=b²-4ac Δ=5²-4*4*(-69) Δ=25+1104 Δ=1129 √Δ=√1129 x₁=-b-√Δ/2a=-5-√1129/8 x₂=-b+√Δ/2a=-5+√1129/8 b) x⁵-x⁴-5x³-6x+6=0 x³(x²-x-5)-6(x+1)=0 (x³-6)(x²-x-5)(x+1)=0 x³-6=0___∧ x²-x-5=0 _____ ∧ x-1=0 x³=6∧_____Δ=b²-4ac∧________x=1 x=³√6 _____Δ=(-1)²-4*1*(-5) ___________Δ=1+20 ____________Δ=21 ____________√Δ=√21 x₁=1-√21/2 x₂=1+√21/2 c)5x⁴ -6x³=0 x³(5x-6)=0 x³=0∧5x-6=0 x=0∧5x=6|5 ____x=1⅕