a) (x+4) 2=x+40; x2+8x+16-3x-40=0; x2+5x-24=0; D=52-4 ⋅ 1 ⋅ (-24)=121; − 5 ± 121 − 5 ± 11 = ; 2 ⋅1 2 −5 + 11 =3; x1= 2 −5 − 11 =-8; x2= 2
x=
б) (2x-3)2=11x-19; 4x2-12x+9-11x+19=0; 4x2-23x+28=0; D=232-4 ⋅ 4 ⋅ 28=81; 23 ± 81 23 ± 9 ; = 8 8 23 − 9 =1,75; x1= 8 23 + 9 =4; x2= 8
x=
в) (x+1)2=7918-2x; x2+2x+1+2x-7918=0; x2+4x=7917=0; D1=22-1 ⋅ (-7917)=4+7917=7921; x=
− 2 ± 7921 =-2 ± 89; 1
x1=-2+89=87; x2=-2-89=-91; г) (x+2)2=3131-2x; x2+4x+4-3131+2x=0; x2+6x-3127=0; D1=9-1 ⋅ (-3127)=9+3127=3136; x=
− 3 ± 3136 = −3 ± 56 ; 1
x1=-3+56=53; x2=-3-56=-59. №546. a) 3(x+4)2=10x+32; 3(x2+8x+16)=10x+32; 3x2+14x+16=0; D1=72-3 ⋅ 16=1; x= x1=
−7 ± 1 ; 3
−7 + 1 =-2; 3
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