x gosc: Oblicz x

	24
sin(4arctg(x)) =
	25

www: 1/2, 1/3, −2, −3

Mariusz: sin(4α)=2sin(2α)cos(2α) sin(4α)=4sin(α)cos(α)(cos²(α)−sin²(α)) sin(4α)=4cos(α)sin(α)(1−2sin²(α)) sin(4α)=4cos(α)(sin(α)−2sin³(α)) sin(4α)=4(sin(α)cos(α)−2sin³(α)cos(α)) sin(4α)=4(sin(α)cos(α)−2sin²(α)(sin(α)cos(α))

	sin(α)
tg(α)=
	cos(α)

tg(α)cos(α)=sin(α) tg(α)cos²(α)=sin(α)cos(α)

	cos2(α)
tg(α)		=sin(α)cos(α)
	cos2(α)+sin2(α)

tg(α)
	=sin(α)cos(α)
1+tg2(α)

	sin(α)
tg(α)=
	cos(α)

tg(α)cos(α)=sin(α) tg²(α)cos²(α)=sin²(α)

	cos2(α)
tg2(α)		=sin2(α)
	cos2(α)+sin2(α)

tg2(α)
	=sin2(α)
1+tg2(α)

sin(4α)=4(sin(α)cos(α)−2sin²(α)(sin(α)cos(α))

	x		2x2		x		24
4(		−		*		)=
	1+x2		1+x2		1+x2		25

x		2x3		6
	−		=
1+x2		(1+x2)2		25

x−x3		6
	=
(1+x2)2		25

25x−25x³=6(1+2x²+x⁴) 6x⁴+25x³+12x²−25x+6=0 * 24 144x⁴+600x³+288x²−600x+144=0 (144x⁴+600x³)−(−288x²+600x−144)=0 (144x⁴+600x³+625x²)−(337x²+600x−144)=0 (12x²+25x)²−(337x²+600x−144)=0

	y		y2
(12x2+25x+		)2−((12y+337)x2+(25y+600)x+		−144)=0
	2		4

	y2
4(		−144)(12y+337)−(25y+600)2=0
	4

(y²−576)(12y+337)−625(y+24)²=0 (y+24)(y−24)(12y+337)−625(y+24)²=0 (y+24)((y−24)(12y+337)−625(y+24))=0 y=−24

	y		y2
(12x2+25x+		)2−((12y+337)x2+(25y+600)x+		−144)=0
	2		4

(12x²+25x−12)²−((−288+337)x²+0x+0)=0 (12x²+25x−12)²−49x²=0 (12x²+25x−12)²−(7x)²=0 ((12x²+25x−12)−7x)((12x²+25x−12)+7x)=0 (12x²+18x−12)(12x²+32x−12)=0 (2x²+3x−2)(3x²+8x−3)=0

	−3−√9+4*2*2
x1=
	2*2

	−3+√9+4*2*2
x2=
	2*2

	−8−√64+4*3*3
x3=
	2*3

	−8+√64+4*3*3
x4=
	2*3

x₁=−2

	1
x2=
	2

x₃=−3

	1
x4=
	3