1) 12x-35-x²=0
-x²+12x-35=0
D= 12²-4*35= 144-140= 4= 2²
x₁= (12+2)/2= 14/2= 7
x₂= (12-2)/2= 10/2= 5
2) x²-11x-42=0
D=(-11)²+ 4*42= 121+168= 289= 17²
x₁= -(11-17)/2= -6/2= -3
x₂= -(11+17)/2= -28/2= -14
3) 2+3x²-4x=0
3x²-4x+2=0
D=(-4)²- 4*3*2= 16-24= -8
Нет корней, т.к. D<0
4) -24x-9-16x²=0
-16x²-24x-9=0
D=(-24)²-4*16*9= 576-576=0
x₀= -24/32= -0.75
5) 5x-x²= 0
-x²+5x=0
D=5²+4*0= 25= 5²
x₁= (5+5)/2=10/2= 5
x₂= (5-5)/2 = 0/2=0
6) -x²+8=0
D= 0²+4*8= 32= √32
x₁=(√32)/2= (4√2)/2= 2√2
x₂=-(√32)/2= -(4√2)/2= -2√2
7) 17a-12-6a²=0
-6a²+17a-12=0
D=17²-4*6*12= 289-288=1=1²
a₁= -(17-1)/12= -16/12= -8/2
a₂= -(17+1)/12= -18/12= -3/2
Объяснение:
1) 12x-35-x²=0
-x²+12x-35=0
D= 12²-4*35= 144-140= 4= 2²
x₁= (12+2)/2= 14/2= 7
x₂= (12-2)/2= 10/2= 5
2) x²-11x-42=0
D=(-11)²+ 4*42= 121+168= 289= 17²
x₁= -(11-17)/2= -6/2= -3
x₂= -(11+17)/2= -28/2= -14
3) 2+3x²-4x=0
3x²-4x+2=0
D=(-4)²- 4*3*2= 16-24= -8
Нет корней, т.к. D<0
4) -24x-9-16x²=0
-16x²-24x-9=0
D=(-24)²-4*16*9= 576-576=0
x₀= -24/32= -0.75
5) 5x-x²= 0
-x²+5x=0
D=5²+4*0= 25= 5²
x₁= (5+5)/2=10/2= 5
x₂= (5-5)/2 = 0/2=0
6) -x²+8=0
D= 0²+4*8= 32= √32
x₁=(√32)/2= (4√2)/2= 2√2
x₂=-(√32)/2= -(4√2)/2= -2√2
7) 17a-12-6a²=0
-6a²+17a-12=0
D=17²-4*6*12= 289-288=1=1²
a₁= -(17-1)/12= -16/12= -8/2
a₂= -(17+1)/12= -18/12= -3/2
Объяснение: