2x^2+9x-5=4x^2-4x+1 2x^2-13x+6=0 Δ=169-4*2*6 Δ=169-48 Δ=121 √Δ=11 x₁=-13-11/4=-6 x₂=13+11/4=-1/2 4x^{2}+4x+1>0 Δ=16-4*4*1 Δ=0 x₀=-4/8=-1/2 5x(x⁴-1)*4(x⁴-1) (5x+4)(x⁴-1)
2 x^2 + 9x - 5 = (2x - 1)^2 2 x^2 + 9 x - 5 = 4 x^2 - 4x + 1 2 x^2 - 13 x + 6 = 0 --------------------- delta =(-13)^2 - 4*2*(6) = 169 + 48 = 121 p(delty) = 11 x = [ 13 - 11]/4 = 2/4 = 1/2 lub x = [13 + 11]/4 = 24/4 = 6 ========================== 4 x^2 + 4x + 1 > 0 ( 2x + 1)^2 > 0 x należy do R { - 1/2} ===================== II sposób: 4 x^2 + 4x + 1 > 0 delta = 4^2 - 4*4*1 = 16 - 16 = 0 x1 = x2 = - 4/8 = - 1/2 a = 4 > 0 => ramiona paraboli skierowane są ku górze, czyli dla x różnych od ( -1/2) 4 x^2 + 4x + 1 > 0 ======================= 5 x^5 + 4 x^4 - 5x - 4 = 0 x^4 *( 5x + 4) - 1*(5x + 4) = 0 ( 5x + 4)*( x^4 - 1 ) = 0 (5x + 4)*(x^2 - 1)*(x^2 + 1) = 0 (5x + 4)*(x -1)*(x +1)*(x^2 + 1) = 0 <=> 5x + 4 = 0 v x+1 = 0 v x - 1 = 0 <=> <=> x = - 4/5 v x = - 1 v x = 1 bo x^2 + 1 >= 0 dla dowolnej liczby rzeczywistej x Odp. x1 = -1, x2 = -4/5, x3 = 1 ===============================
