Question

Rozwiąz równania:

a)2x⁷+x⁶-3x⁵=0

b)x³-3x²-5x+15=0

Answer 1

a)

2x⁷+x⁶-3x⁵ = 0

x⁵(2x²+x-3) = 0 

x = 0

lub

2x²+x-3 = 0

Δ = b²-4ac = 1+24 = 25

√Δ = 5 

x1 = (-b-√Δ)/2a = (-1-5)4 = -6/4 = -1,5

x2 = (-b+√Δ)/2a = (-1+5)/4 = 4/4 = 1

Odp.  x = -1,5   v   x = 0   v   x = 1

 

b)

x³-3x²-5x+15 = 0

x²(x-3)-5(x-3) = 0

(x-3)(x²-5) = 0

(x-3)(x+√5)(x-√5) = 0

x = 3   v  x = -√5   v   x = √5

Odp. x = -√5   v   x = √5   v   x = 3