Объяснение:
Решите уравнение:
1) х^2 – 5х – 12 = 6;
х^2 – 5х – 12 -6 =0;
х^2-5х-18 =0;
a=1; b=-5; c=-18;
D=b^2-4ac=(-5)^2-4*1*(-18)=25+72=97>0 - 2 корня.
x1,2=(-b±√D)/2a=(-(-5)±√97)/2*1=(5±√97)/2;
x1=(5+√97)/2;
x2=(5-√97)/2.
3) х²+ 8x = -16 – 2x;
x^2+10x+16=0;
по т. Виета
x1+x2=-10;
x1*x2=16;
x1=-2; x2=-8.
2) х^2-5х-4 = 10;
х^2-5х-14=0;
по т. Виета
x1+x2=5; x1*x2=-14;
x1=-2; x2=7.
4) х^2 + х – 2 = 2 – 2x;
x^2+3x-4=0;
по т. Виета
x1+x2=-3; x1*x2=-4;
x1=1; x2=-4.
6) 9x - x2 = 6 + 2x;
-x^2+7x-6=0; [*(-1)]
x^2-7x+6=0;
по т. Виета
x1+x2=7; x1*x2=6;
x1=1; x2=6.
8) x — 2х2 + 7 = -1 – 5x;
-2x^2+6x+8=0; [:(-2)]
x^2-3x-4=0;
по т. Виета
x1+x2=3; x1*x2=-4;
x1=-1; x2=4.
5) -х^2 + 3х – 12 = — 4x;
-x^2+7x-12=0; [*(-1)]
x^2-7x+12=0
по т. Виета
x1+x2=7; x1*x2=12;
x1=3; x2=4.
7) - x^2 + 5х = 18 — 6x;
-x^2+11x-18=0; [*(-1)]
x^2-11x+18=0;
по т. Виета
x1+x2=11; x1*x2=18;
x1=2; x2=9.
9) 2x - 3x^2 + 8 = -1 - 6x.
-3x^2+8x+9=0; [*(-1)]
3x^2-8x-9=0;
a=3; b=-8; c=-9;
D=b^2-4ac=(-8)^2-4*3*(-9)=64+108=172>0 - 2 корня.
x1,2=(-b±√D)/2a=(-(-8)±√172)/2*3=(8±2√43)/6=(4±√43)/3;
x1=(4+√43)/3;
x2=(4-√43)/3.
Объяснение:
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а) f'(x)=-2/x^2, f'(x0)=-2/(-1)^2=-2/1=-2
б) f'(x)=4/x^2, f'(x0)=4/2^2=4/4=1