Question

(x-4)V(x+1)<4-2x

V(x+1) -znaczy pierwiastek z( )

Answer 1

(x-4)*√(x+1) < 4-2x  I² 

 Z: x ≥ -1

(x+1)*(x-4)² < (4-2x)² 

(x+1)(x²-8x+16) < 16-16x+4x²

x³-8x²+16x+x²-8x+16 < 4x²-16x+16

x³-8x²+16x+x²-8x+16 < 4x²-16x+16

x³-11x²+24x < 0

x(x²-11x+24) < 0

Przyrównujemy do zera

x(x²-11x+24) = 0

x = 0   => x < 0 

x²-11x+24 = 0

Δ = b²-4ac = 11² - 4*24 = 121-96 = 25

√Δ = 5 

x1 = (-b-√Δ)/2a = (11-5)/2 = 6/2 = 3

x2 = (-b+√Δ)/2a = (11+5)/2 = 16/2 = 8

x ∈<-1;0) u (3;8)

 

 

 

Answer 2