3х-12-7х=8
-4х-12=8
-4х=8+12
-4х=20
х=-5
Решение по действиям :
1.
3 3 3х¹/⁴ - 3у¹/⁴+ 3х¹/⁴ +3 у¹/⁴ 6х¹/⁴
-------------- + ------------- = ------------------------------------ = -----------------
х¹/⁴ + у¹/⁴ х¹/⁴ - у¹/⁴ (х¹/⁴)² - (у¹/⁴)² х¹/² - у¹/²
2.
6х¹/⁴ у⁻¹/² - х⁻¹/² 6х¹/⁴ *( у⁻¹/² - х⁻¹/²) *х¹/⁴у¹/²
---------------- * --------------------- = ----------------------------------------------- =
х¹/² - у¹/² 4х⁻¹/⁴у⁻¹/² (х¹/² - у¹/²)* 4
6 *( у⁻¹/² - х⁻¹/²) *х¹/²у¹/² 6*(х¹/² -у¹/²) 6
= ----------------------------------- = ------------------------- = ------- = 1,5
(х¹/² - у¹/²)* 4 (х¹/² - у¹/²)* 4 4
2. (а-3)(а+3) = а^2 - 3^2 = а^2 - 9;
(2у+5)(2у-5) = (2у)^2 - 5^2 = 4y^2 - 25;
3. (6x-x^2)^2-x^2(x-1)(x+1)+6x(3+2x^2) = 36x^2 - x^4 - x^4 + x^2 + 18x + 12x^3 = 37x^2 - 2x^4 + 18x + 12x^3
3. (x-4)(x^2 + 4x + 16) = x^3 - 4x^2 + 4x^2 - 16x + 16x - 64 = x^3 - 64 = (x-64)(x^2 - 4x + 16)
Надо называть те числа в которых нет тройки. И те числа, которые не делятся на 3 ( не кратны трем) Например: 1, 2, 4, 5, 7, 8 ........ 25, 26, 28, 29, ...... 112, 113 и т.д.
А)
4cos a/2*cos b/2*cos y/2 = sin a + sin b + sin y
---
4cos α/2*cos β/2*cosγ/2 =
2(cos(α+β)/2 +cos(α-β)/2)*cosγ/2 =
2cos(α+β)/2*cosγ/2 +2cosγ/2 *cos(α-β)/2=
cos(α+β+γ)/2 +cos(α+β-γ)<span>/2+</span>cos(α+γ-β)/2 +cos(γ+β-α)<span>/2 =
</span>cosπ/2 +cos(α+β+γ -2γ)/2+cos(α+β+γ-2β)/2 +cos(β+γ+α-2α)/2=
cos(π -2γ)/2+cos(π-2β)/2 +cos(π-α)/2=
cos(π/2 -γ)+cos(π/2-β) +cos(π/2-α) = sinα +sinβ+sinγ.
----------
б) 4sin(α/2)*sin(β/2)*cos(γ/2) = sin α + sin <span>β</span> - sin γ
---
sin α + sin β - sinγ =2sin((α+c)/2)*cos((α-β)/2) -sin(π-(α+<span>β))=
</span>2sin((α+β)/2)*cos((α-β)/2) -sin(α+<span>β)=
</span>2sin((α+β)/2)*cos((α-β)/2) -sin2*((α+<span>β)/2)=
</span>2sin((α+β)/2)*cos((α-β)/2) -2sin((α+β)/2)*cos((α<span>+β)/2) =
</span>2sin((α+β)/2)*(cos((α-β)/2) -cos((α<span>+β)/2) )=
</span>2sin((π-γ)/2) *(-2sin(α/2)*sin(-β/2) =2sin(π/2-γ/2) *2sin(α/2)*sin(β/2)=
2cos(γ/2) *2sin(α/2)*sin(β/2) =4sin(α/2)*sin(β/2)*cos(γ/2) .