1.Rozwiąż równanie wielomianowe: a)[latex] x^{4} +3 x^{2} -14+2 x^{2} =0[/latex] b)[latex] x^{3}-27=(x+3)( x^{2} +9)[/latex] 2.Rozwiąż równania: a)[latex] frac{x+1}{4x} = frac{1}{x-1} [/latex] b)[latex] frac{4x-1}{5x-2} =0[/latex]

x⁴+3x²-14+2x²=0 x⁴+5x²-14=0 x²=t t≥0 t²-5t-14=0 t₁+t₂=5 t₁t₂= -14 t₁= -7<0 t₂=2 t=2 x=√t=√2 x³-27=(x+3)(x²+9) x³-3³=(x+3)(x²+3²) (x-3)(x²-3x+9)=(x+3)(x+3)(x-3) x²-3x+9=(x+3)(x+3) x²-3x+9=x²-6x+9 x²-x²-3x+6x=9-9 3x=0 x=0 [latex] frac{x+1}{4x} = frac{1}{x-1} \ (x+1)(x-1)=4x*1 \ x^2-1=4x \ x^{2} -4x-1=0 \з=(-4)^2-4*1*(-1)=16+4=20=4*5=2^2*5 \ x_1= frac{4-2 sqrt{5} }{2} = frac{2(2- sqrt{5} )}{2} =2- sqrt{5} \ x_2= frac{4+2 sqrt{5} }{2} = frac{2(2+sqrt{5} )}{2} =2+ sqrt{5} \ \ [/latex] [latex] frac{4x-1}{5x-2} =0 \ left { {{4x-1=0} atop {5x-2 eq 0}} ight. \ left { {{4x=1} atop {5x eq 2}} ight. \ left { {{x= frac{1}{4} } atop {x eq frac{2}{5} }} ight. \ left { {{x= 0.25 } atop {x eq0.4}} ight. [/latex]

1. Rozwiaż równania wielomianowe a) [latex] 8x^{6} [/latex] + [latex] 15x^{5} [/latex] = [latex]2 x^{4} [/latex] b) [latex] frac{1}{4} x^{6} [/latex] = [latex] 9x^{2} [/latex] 2. Rozwiąż równanie [latex] frac{x-1}{x+1} = frac{x-2}{x-5} [/latex]

1. Rozwiaż równania wielomianowe a) [latex] 8x^{6} [/latex] + [latex] 15x^{5} [/latex] = [latex]2 x^{4} [/latex] b) [latex] frac{1}{4} x^{6} [/latex] = [latex] 9x^{2} [/latex] 2. Rozwiąż równanie [latex] frac{x-1}{x+1} = frac{x-2}{x-5} ...