1)(x²-9)/(16x²-8x+1)>0
(x-3)(x+3)/(4x-1)²>0
(4x-1)²>0;=>x€(-oo;1/4)U(1/4;+oo)
(x-3)(x+3)>0;=>x€(-oo;-3)U(3;+oo)
__-3_______1/4________3____
=>x€(-oo;-3)U(3;+oo)
2){3-x>0;x<3
{3-x≠1;x≠4
=>x<3
3){x<3
{x€(-oo;-3)U(3;+oo);=>x€(-oo;-3)
<span>task/26474004
--------------------
Разложить квадратный трехчлен на множители:
а) x</span>² <span>- 7x + 10
б) 7x</span>²<span> + 20x - 3
в) 12x</span>²<span> - 588
* * * ax</span>²+bx +c =a(x -x₁)(x-x<span>₂) * * *
</span>а) x² - 7x + 10 =x² - 7x + 10 = (x² - 2x) -(5x +10 ) =x(x-2) -5(x-2) =(x-2)(x-5).
* * *
x² -7x +10 =0 ; D =7² - 4*1*10 = 49 - 40 =9 =3²
x₁ =(7-3)/2*1 =4/2=2;
x<span>₂=(7+3)/2 =5 . (x -2)(x-5)
* * *
</span>б) 7x² + 20x - 3 =7(x +3)(x - 1/7) || (x +3)(7x - 1) ||
* * *
7x² +20x -3=0 ; D₁ =10² - 7*(-3) = 100+21=121=11²
x₁ =(-10 -11) /7 =-21/7 = -3 ;
x₂=(-10 +11) /7 = 1/7. (x -(-3)) (x -1/7) =7(x+3)(x -1/7) = (x+3)(7x -1).
--------
в) 12x² - 588 =12(x² - 49)=12(x² - 7²) =12(x - 7) (x + 7) .
(х-3)(х+4)-(х-2)(х+3) =
=(х²+4х-3х-12) - (х²+3х-2х-6)=
= х²+х-12-х²-х+6=
= -12+6=-6
2
a)208 3 четверть
sin208<0, cos208<0,tg208>0,ctg208>0
sin208*cos208*tg208*ctg208>0
b)3,1 2 четверть
sin3,1>0,cos3,1<0,tg3,1<0,ctg3,1<0
sin3,1*cos2,1*tg3,1*ctg3,1<0
3
2cos²-3=cos2x-2
-1≤cos2x≤1
-1-2≤cos2x-2≤1-2
-3≤cos2x-2≤-1
4
cos10x=√2/2
10x=+-π/4+2πn
x=+-π/40+πn/5