a) (x-3)² = 25 x²-6x+9=25 x²-6x+9-25=0 x²-6x-16=0 ∆= b²-4ac ∆=(-6) ²-4x1x(-16) ∆=36+64 ∆=100 √∆=10 -b+ √∆ 6+10 16 x1=---------=--------=----=8 2a 2x1 2 -b+ √∆ 6-10 -4 x2=---------=--------=----=-2 2a 2x1 2 b)4(3x+2)² = 8 4(9 x²+12x+4)=8 36x²+48x+16=8 36x²+48x+16-8=0 36x²+48x+8=0 ∆= b²-4ac ∆=48²-4x36x8 ∆=2304-1152 ∆=1152 -b+ √∆ -48+1152 1104 x1=---------=-------------=--------=15 24/72 2a 2x36 72 -b+ √∆ -48-1152 -1200 x2=---------=------------=---------=-16 48/72 2a 2x36 72 c) ⅓ (6-5x) ² = 0 ⅓(36-60x+25x²)=0 12-20x+25/3 x²=0 25/3 x²-20x+12=0 ∆= b²-4ac ∆=(-20)²-4x(25/3)x12 ∆=400-400 ∆=0 -b 20 20 x1= x2=-------=---------=----=20x3/50=6/5 2a 2x25/3 50/3 d) (0,2x-3)² = -1,4 0,04x²-1,2x+9=1,4 0,04x²-1,2x+9-1,4=0 0,04x²-1,2x+7,6=0 4/100 x²-12/10x+76/10=0/ to mnoży przez100 4 x²-120x+760=0 ∆= b²-4ac ∆=(-120)²-4x4x760 ∆=14400-12160 ∆=2240 -b+ √∆ 120+2240 2360 x1=---------=-------------=--------=295 2a 2x4 8 -b+ √∆ 120-2240 -2120 x2=---------=------------=---------=-265 2a 2x4 8 e) -3(5x+½)² = 2 -3(25x²+5x+1/4)=2 -75 x²-15x-3/4=2 /to mnożymy x4 -300 x²-60x-3=8 -300 x²-60x-3-8=0 -300 x²-60x-11=0 ∆= b²-4ac ∆=(-60)²-4x(-300)x(-11) ∆=3600-13200 ∆=-9600 brak mjesc zarowych bo ∆ jest na minusie f) -0,3(0,7x+1)² = -6 -3/10(7/10x+1) ²=-6 -3/10(49/100x²+14/10x+1)=-6 -147/1000x²-42/100x-3/10=-6 / to mn x1000 -147x²-420x-300=-6000 -147x²-420x-300+6000=0 -147x²-420x-5700=0 ∆= b²-4ac ∆=(-420)²-4x(-147)x(-5700) ∆=176400-3351600 ∆=-3175200 brak miejsc zerowych g) x²-4x+1 = 0 ∆= b²-4ac ∆=(-4)²-4x1x1 ∆=16-16 ∆=0 -b 4 4 x1= x2=---=----=---=2 2a 2x1 2 h) x²+6x-7 = 0 ∆= b²-4ac ∆=6²-4x1x(-7) ∆=36+28 ∆=64 √∆=8 -b+ √∆ -6+8 2 x1=---------=--------=----=1 2a 2x1 2 -b+ √∆ -6-8 -14 x2=---------=--------=----=-7 2a 2x1 2 i) x² +3x-2,5 = ∆= b²-4ac ∆=3²-4x1x(-2,5) ∆=9+10 ∆=19 -b+ √∆ -3+19 16 x1=---------=--------=----=8 2a 2x1 2 -b+ √∆ -3-19-22 x2=---------=--------=----=-11 2a 2x1 2
