Rozwiąż równania a) 2√5 x < 2x+1 b) 3x+3 ≤ πx + π

Rozwiąż równania a) 2√5 x < 2x+1 2√5x - 2x < 1 (2√5 -2)*x < 1 /:(2√5 -2) x < 1 : (2√5 -2) x < [1 : (2√5 -2)]*[(2√5 +2):(2√5 +2)] usuwam niewymierność mianownika x < (2√5 +2) : [ (2√5)² - 2²] x < 2(√5 +1) : (20 -4) x < 2(√5 +1) : 16 x < (√5 +1) :8 x < (1/8)*(√5 +1) x < 1/8*√5 + 1/8 ( tj ok. 0,405) spr. L(0) = 2√5*0 = 0 P(0) = 2*0 +1 = 1 L(0) < P(0) b) 3x+3 ≤ πx + π 3x - πx ≤ π -3 - πx + 3x ≤ π -3 -(π -3)x ≤ π -3 /: [-( π -3)] x ≥ (π -3) : [-(π -3)] x ≥ -1 L(-1) = 3*(-1) +3 = -3 +3 = 0 P(-1) = π*(-1) + π = -π + π = 0 L(-1) = P(-1) L(0) = 3*0 + 3 = 3 P(0) = π*0 + π = π ≈ 3,14 P(0) < L(0)

a) 2V5 x <2x +2/^ (^ do kwadratu) (2V5 x)^< (2x +2)^ 20 x^< 4x^ + 8x +4 20 x^- 4 x^ - 8 x - 4 < 0 16 x^- 8 x - 4 < 0 /: 4 4 x^ -2 x -1 < 0 D = b^ - 4*a*c D = 4 +16 =20 VD =2V5 X1 = (2 - 2V5)/8 = 2(1- V5)/8 = (1- V5)/4 X2 = (2 +2V5)/8 = 2(1+V5)/8 = (1+ V5)/4 X < (1+V5)/4 b) 3x +3 <= pi x + pi 3x - pi x <= pi -3 -pi x +3x <= pi -3 -(pi -3)x <= pi -3 /:[-(pi -3)] X >= -1