1.
√3 + tg15° = √3 + tg(45°-30°) = √3 + tg45° - tg30°/1 + tg45°×tg30° = √3 + 1 - √3/3 / 1 + 1×√3/3 = √3 + 1 - √3/3 / 1 + √3/3 = √3 + 3-√3/3 / 3+√3/3 = √3 + 3-√3/3+√3 = √3 + (3 - √3)×(3 - √3)/6 = √3 + (3 - √3)²/6 = √3 + 9 - 6√3 + 3/6 = √3 + 12-6√3/6 = √3 + 6(2-√3)/6 = √3+2-√3 = 2
ответ: d) 2
2.
8sin15° × cos15° + √3 × tg60° = 4sin30° + √3 × √3 = 4×1/2 + (√3)² = 2+3 = 5
ответ: c) 5
3.
а) tg225° + sin30° = tg(180°+45°) + 1/2 = tg45° + 1/2 = 1 + 1/2 = 3/2 = 1,5
б) √2 × cos315° = √2 × cos(360°-45°) = √2 × cos(-45°) = √2 × cos45° = √2 × √2/2 = (√2)²/2 = 2/2 = 1
ответ: а) 1,5 б) 1
1. 3(5x + 6y)
2. y( 3x - 5)
3. a^4( 1 + a^5)
4. 2y( y^4 - 2y^2)
5. 5a( b + 2a)
6. (2 - a) ( 5 + 3a)
7. (x + 3) (x - y)
8. (x - 6)(2x + 3 - x - 6) = (x - 6)(x - 3)
1) 8x - x^2 = 0, x(8 - x) = 0
либо x = 0, либо 8 - x = 0
ответы: x =0 , x = 8.
2) (3 - x)(2x - 4) - (2x - 4)(5 + x) = 0
(2x - 4)( 3 - x - 5 - x) = 0
(2x - 4)(-2x - 2) = 0
x = 2 , x = -1
Объяснение: