" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
-x⁷-3x⁶+18x⁵=0
x⁵(-x²-3x+18)=0
x⁵=0
x=0
-x²-3x+18=0
Δ=(-3)²-4*(-1)*18=9+72=81
√Δ=9
x₁=(3+9)/-2=12/-2=-6
x₂=(3-9)/-2=-6/-2=3
b)16x⁷+8x⁵+x³=0
x³(16x⁴+8x²+1)=0
x³=0
16x⁴+8x²+1=0
(4x²+1)² =0
4x²+1=0
4x²=-1
x²=-1/4
brak rozwiązania
c) 2x³+3=x²+6x
2x³-x²-6x+3=0
-x²(-2x+1)+3(-2x+1)=0
(-x²+3)(-2x+1)=0
-x²+3=0
-x²=-3
x²=3
x=√3 lub x=-√3
-2x+1=0
-2x=-1
x=½
-x⁷-3x⁶+18x⁵=0
-x⁵(x²+3x-18)=0
Δ=9+4*18=81
x₁=(-3-9)/2=-6
x₂=(-3+9)/2=3
-x⁵(x+6)(x-3)=0
x=0 v x=-6 v x=3
16x⁷+8x⁵+x³=0
x³(16x⁴+8x²+1)=0
niech x²=t
x³(16t²+8t+1)=0
Δ=64-4*16=0
t₀=-8/(2*16)=-¼
t₀<0 - nie ma pierwiastka kwadratowego
x³(t+¼)²=0
x=0
2x³+3=x²+6x
2x³-x²-6x+3=0
x²(2x-1)-3(2x-1)=0
(2x-1)(x²-3)=0
(2x-1)(x-√3)(x+√3)=0
x=½ v x=√3 v x=-√3
x³-5x-4=0
dzielniki wyrazu wolnego:
p: ±1, ±2, ±4
z tw. Bezouta
W(-1)=(-1)³-5*(-1)-4=-1+5-4=0
schemat Hornera
__|1| 0|-5|-4
-1|1|-1|-4| 0
(x+1)(x²-x-4)=0
Δ=1+16=17
x₁=1-√17/2
x₂=1+√17/2
x=-1 v x=1-√17/2 v x=1+√17/2