x²-1+x=1 x²+x-2=0 a=1; b=1; c=-2 Δ=b²-4ac Δ = 1-4*1*(-2)=1+8=9 √Δ=3 x₁ = (-1-3) / (2*1) = -4/2 = -2 x₂ = (-1+3) / (2*1) = 2/2 =1 _______________________________________________________________ 20+x2-8Xx=5 x²+8x+20-5=0 x²+8x+15=0 a=1; b=8; c=15 Δ=b²-4ac Δ = 64-4*1*15=64-60=4 √Δ=2 x₁ = (-8-2) / (2*1) = -10/2 = -5 x₂ = (-8+2) / (2*1) = -6/2 = -3 _______________________________________________________________ To jest ułamek - 15 (kreska ułamkowa)x+1=3 x+1≠0 ⇒ x≠-1 -15 / (x+1) = 3 3(x+1)=-15 3x+3 = -15 3x = -15-3 3x = -18 I:3 x = -18/3 x= -6 _______________________________________________________________ 2Xx=x+5 2x = x+5 2x-x = 5 x=5 __________________________________________________________________ x2-4=x+2 x²-4-x-2=0 x²-x-6=0 a=1; b=-1;c=-6 Δ=b²-4ac Δ = 1-4*1*(-6)=1+24=25 √Δ=5 x₁ = (1-5) / (2*1) = -4/2 = -2 x₂ = (1+5) / (2*1) =6/2=3 _______________________________________________________________ 5X(3+a)=aX10 15+5a = 10a 5a-10a=-15 -5a = -15 I:(-5) a=3 ___________________________________________________________________ x2+3=4Xx x²-4x+3=0 a=1; b=-4;c=3 Δ=b²-4ac Δ = 16-4*1*3=16-12=4 √Δ=2 x₁ = (4-2) / (2*1) = 2/2 = 1 x₂ = (4+2) / (2*1) =6/2=3 _____________________________________________________________ x2-1=8 x²-1-8=0 x²-9=0 x²-3²=0 (x-3)(x+3)=0 x-3=0⇒x=3 ∨ x+3=0 ⇒x=-3 __________________________________________________________________ (x-1)X(x+1)=x2-1 x²-1=x²-1 x²-1-x²+1=0 0=0 Rozwiązaniem jest zbiór wszystkich liczb rzeczywistych R
