Выражение под корнем должно быть >= 0.
(4x + 5)(3 - x) >= 0.
4x + 5 = 0 при x = -5/4
3 - x = 0 при x = 3
Произведение >= 0 при 4x + 5 >= 0 и 3 - x >= 0, то есть при x >= -5/4 и x <= 3.
Ответ: [-5/4; 3]
6.
sin51°cos39°-sin21°cos9°=sin(90°-39°)cos39°-sin21°cos9<span>°=
=cos39</span>°cos39°-sin(30°-9°)cos9°=cos²39°-sin(30°-9°)cos9<span>°=
=(cos(30</span>°+9°))² - (sin30°cos9°-cos30°sin9°)cos9<span>°=
=(cos30</span>°cos9°-sin30°sin9°)² - (¹/₂ cos9° - (√3/2) sin9°)cos9<span>°=
=((</span>√3/2) cos9° - ¹/₂ sin9°)² - ¹/₂ cos² 9° + (√3/2) sin9° cos9<span>° =
= </span>³/₄ cos² 9° - (√3/2)sin9° cos9° + ¹/₄ sin² 9° - ¹/₂ cos² 9° + +(√3/2)sin9°cos9<span>°=
= </span>³/₄ cos² 9° - ²/₄ cos² 9° + ¹/₄ sin² 9<span>° =
= </span>¹/₄ cos² 9° + ¹/₄ sin² 9<span>° =
= </span>¹/₄ (cos² 9° + sin² 9<span>°</span>)= ¹/₄ * 1 = ¹/₄
-3n+3m це точно правильно
1. (3ⁿ+3ⁿ⁻¹)²=(3ⁿ+3ⁿ/3)²=(3ⁿ+(3ⁿ/3))²=((3*3ⁿ+3ⁿ)/3)²=(4*3ⁿ/3)²=(4*3ⁿ⁻¹)²=16*3²ⁿ⁻².
2. 9ⁿ⁻¹=3²*⁽ⁿ⁻¹⁾=3²ⁿ⁻².
3. 16*3²ⁿ⁻²/3²ⁿ⁻²=16.